{"id":36059,"date":"2023-11-10T20:47:00","date_gmt":"2023-11-10T20:47:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36059"},"modified":"2023-11-16T10:13:36","modified_gmt":"2023-11-16T10:13:36","slug":"volume-of-a-right-circular-cone-definition-formula-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone","title":{"rendered":"Volume of a Right Circular Cone \u2013 Definition, Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-0da4fd18-c1a8-4dc1-b7ee-0b2ad042c78f\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#0-what-is-the-volume-of-a-right-circular-cone>What Is the Volume of a Right Circular Cone?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#1-volume-of-right-circular-cone-formula>Volume of Right Circular Cone Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#2-how-to-find-the-volume-of-a-right-circular-cone>How to Find the Volume of a Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#5-solved-examples-on-volume-of-a-right-circular-cone>Solved Examples on Volume of a Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#6-practice-problems-on-volume-of-a-right-circular-cone>Practice Problems on Volume of a Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone#7-frequently-asked-questions-about-volume-of-a-right-circular-cone>Frequently Asked Questions about Volume of a Right Circular Cone<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-volume-of-a-right-circular-cone\">What Is the Volume of a Right Circular Cone?<\/h2>\n\n\n\n<p><strong>The <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/volume\"><strong>volume<\/strong><\/a><strong> of a right circular cone is the total space occupied by the right circular cone. It is equal to one-third the product of the base area and height.<\/strong><\/p>\n\n\n\n<p>The formula to find the volume of a right circular cone is $V = \\frac{1}{3} \\pi r^{2}h$, where r is the radius of the base <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/circle\">circle<\/a> and h is the height of the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/cone\">cone<\/a>.<\/p>\n\n\n\n<p>A right circular cone is a type of cone in which the axis of the cone is the line joining the vertex (apex) and the midpoint of the circular base. A right circular cone is generated by a revolving right triangle about one of its legs.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"566\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/right-circular-cone.png\" alt=\"Right circular cone\" class=\"wp-image-36062\" title=\"Right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/right-circular-cone.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/right-circular-cone-300x274.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>We know that the volume of a cylinder is given by $\\pi r^{2}h$, where r is the radius and h is the height. Thus, we can say that the volume of a cylinder is three times that of a cone having the same radius and height. Three such cones can fill up the cylinder.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"783\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/volume-of-a-cone-and-volume-of-a-cylinder-comparison.png\" alt=\"Volume of a cone and volume of a cylinder comparison\" class=\"wp-image-36063\" title=\"Volume of a cone and volume of a cylinder comparison\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/volume-of-a-cone-and-volume-of-a-cylinder-comparison.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/volume-of-a-cone-and-volume-of-a-cylinder-comparison-238x300.png 238w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/estimate-the-volume-of-a-given-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_estimate_vol_1_pt.png\" alt=\"Estimate the Volume of a Given Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Estimate the Volume of a Given Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_1_pt.png\" alt=\"Find Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-volume-of-the-3d-shape-by-iterating\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_iterate_vol_1_pt.png\" alt=\"Find the Volume of the 3D Shape by Iterating Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Volume of the 3D Shape by Iterating Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-volume-using-unit-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_vol_unit_cubes_2_pt.png\" alt=\"Find the Volume using Unit Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Volume using Unit Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-volume-using-the-formula\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_vol_formula_pt.png\" alt=\"Find Volume using the Formula Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Volume using the Formula Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-cones-and-cubes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_cones_cubes_pt.png\" alt=\"Identify Cones and Cubes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Cones and Cubes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-if-the-given-angle-is-right-acute-or-obtuse\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_type_of_angle_pt.png\" alt=\"Identify if the Given Angle is Right, Acute or Obtuse Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify if the Given Angle is Right, Acute or Obtuse Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_2_pt.png\" alt=\"Identify Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/introduction-to-volume\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_vol_unit_cubes_1_pt.png\" alt=\"Introduction to Volume Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Introduction to Volume Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/iterate-and-find-the-total-volume\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_iterate_vol_2_pt.png\" alt=\"Iterate and Find the Total Volume Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Iterate and Find the Total Volume Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-volume-of-right-circular-cone-formula\">Volume of Right Circular Cone Formula<\/h2>\n\n\n\n<p>Volume of a right circular cone $= \\frac{1}{3} \\pi r^{2}h$<\/p>\n\n\n\n<p>where&nbsp;<\/p>\n\n\n\n<p>r = radius of the circular base<\/p>\n\n\n\n<p>h = height of the cone<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/cones-and-spheres\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/cones-and-spheres.jpeg\" alt=\"Cones and Spheres Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-how-to-find-the-volume-of-a-right-circular-cone\"><br>How to Find the Volume of a Right Circular Cone<\/h2>\n\n\n\n<p>Let\u2019s understand how to calculate the volume of a right circular cone based on the provided information.<\/p>\n\n\n\n<p><strong>Finding Volume Using Radius and Slant Height of a Cone<\/strong><\/p>\n\n\n\n<p>If we know the radius and slant height of the cone, we will first find the height using the<br>formula: $h = \\sqrt{l^{2}\\;-\\;r^{2}}$<\/p>\n\n\n\n<p>Once we know the height, we can calculate the volume as<\/p>\n\n\n\n<p>Volume of the cone $= \\frac{1}{3} r^{2} h = \\frac{1}{3} \\pi r^{2}\\sqrt{l^{2}\\;-\\;r^{2}}$.<\/p>\n\n\n\n<p>This is the formula for the volume of a right circular cone with slant height.<\/p>\n\n\n\n<p><strong>Finding Volume Using Height and Slant Height of a Cone<\/strong><\/p>\n\n\n\n<p>If we know the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/height\">height<\/a> and slant height of the cone, we will first find the radius using the formula:<\/p>\n\n\n\n<p>$r = \\sqrt{l^{2}\\;-\\;h^{2}}$<\/p>\n\n\n\n<p>Once we know the radius, we can calculate the volume as<\/p>\n\n\n\n<p>Volume of the cone $= \\frac{1}{3} \\pi r^{2}h$&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-volume-of-a-right-circular-cone\">Facts about Volume of a Right Circular Cone<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The volume of a right circular cone is exactly one-third of the volume of a cylinder with the same base radius and height.<\/li>\n\n\n\n<li>If we keep the height constant, a cone with a larger base area will have a larger volume, while a cone with a smaller base area will have a smaller volume.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned how to find the volume of a right circular cone, its formula, and different ways of calculating it. Let\u2019s use the formula to solve a few problems and objective questions based on the concept of volume of a right circular cone.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-volume-of-a-right-circular-cone\">Solved Examples on Volume of a Right Circular Cone<\/h2>\n\n\n\n<p><strong>1. A cylinder and a cone have the same radius and same height. If the volume of a cylinder is 1037 cubic inches, what is the volume of the cone?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Volume of cone $= \\frac{1}{3}\\times$ Volume of cylinder<\/p>\n\n\n\n<p>Volume of cone $= \\frac{1}{3} \\times 1038$&nbsp;<\/p>\n\n\n\n<p>Volume of cone = 346 cubic inches.<\/p>\n\n\n\n<p><strong>2. Find the volume of the right circular cone if the radius is 7 units and height is 9 units.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Radius of the cone (r) = 7 units<\/p>\n\n\n\n<p>Height of the cone (h) = 9 units<\/p>\n\n\n\n<p>Volume $= \\frac{1}{3} \\pi r^{2} h$<\/p>\n\n\n\n<p>Volume $= \\frac{1}{3} \\times \\frac{22}{7} \\times 7 \\times 7 \\times 9$&nbsp;<\/p>\n\n\n\n<p>Volume = 462 cubic units.<\/p>\n\n\n\n<p><strong>3. What is the volume of a conical tent whose radius is 14 feet and height is 12 feet?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Radius of the conical tent (r) = 14 feet<\/p>\n\n\n\n<p>Height of the conical tent (h) = 12 feet<\/p>\n\n\n\n<p>Volume of the cone $=&nbsp;\\frac{1}{3} \\pi r^{2}h$<\/p>\n\n\n\n<p>$V = \\frac{1}{3} \\times \\frac{22}{7} \\times 14 \\times 14 \\times 12$&nbsp;<\/p>\n\n\n\n<p>$V = 2464$ cubic feet.<\/p>\n\n\n\n<p><strong>4. If the volume of the right circular cone is <\/strong>24.5\u03c0<strong> cubic inches and height is 6 inches, then what will be the radius of the cone?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Volume of the cone = 24.5\u03c0<strong> <\/strong>cubic inches<\/p>\n\n\n\n<p>Height of the cone (h) = 6 inches<\/p>\n\n\n\n<p>$\\frac{1}{3} \\pi r^{2} h = 24.5$<\/p>\n\n\n\n<p>$\\frac{1}{3} r^{2} \\times 6 = 24.5$<\/p>\n\n\n\n<p>$2r^{2} = 24.5$<\/p>\n\n\n\n<p>$r^{2} = \\frac{24.5}{2} = 12.25$<\/p>\n\n\n\n<p>r = 3.5 inches<\/p>\n\n\n\n<p><strong>5. The volume of the right circular cone is 980 cubic inches. What is the height of the cone if the base radius is 7 inches?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Volume of the cone = 980<strong> <\/strong>cubic inches<\/p>\n\n\n\n<p>Radius of the cone (r)=7 inches<\/p>\n\n\n\n<p>$\\frac{1}{3} \\pi r^{2} h = 980$<\/p>\n\n\n\n<p>$\\frac{1}{3} \\times 7 \\times 7 \\times h = 980$<\/p>\n\n\n\n<p>$\\frac{49h}{3} = 980$<\/p>\n\n\n\n<p>$h = \\frac{980 \\times 3}{49} = 60$ inches<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-volume-of-a-right-circular-cone\">Practice Problems on Volume of a Right Circular Cone<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Volume of a Right Circular Cone \u2013 Definition, Formula, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The slant height of the right circular cone is 13 inches and radius is 5 inches. What is the height of the cone?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">18 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">20 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">24 inches<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 12 inches<br\/>Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$h = \\sqrt{l^{2}\\;-\\;r^{2}}$<br>\r\n$h = \\sqrt{13^{2}\\;-\\;5^{2}} = \\sqrt{169\\;-\\;25} = \\sqrt{144} = 12$ inches<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find the volume of a right circular cone in terms of radius if radius is equal to the height.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{3} \\pi r^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\pi r^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{3} \\pi r^{4}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{3} \\pi r^{3}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{3} \\pi r^{3}$<br\/>Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $= \\frac{1}{3} \\pi r^{2} r = \\frac{1}{3} \\pi r^{3}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If the height of the cone is 18 inches and base diameter is 14 inches, then what will be the volume of the cone?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1024 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">984 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">964 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">924 cubic inches<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 924 cubic inches<br\/>Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $= \\frac{1}{3} \\pi r^{2} h$<br>\r\n$= \\frac{1}{3} \\times \\frac{22}{7} \\times 7 \\times 7 \\times 18 = 924$ cubic inches.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If the volume of the cone is 100 cubic units, and height is 12 units, then what will be the lateral height?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10 units<\/div><div class=\"spq_answer_block\" data-value=\"1\">12 units<\/div><div class=\"spq_answer_block\" data-value=\"2\">13 units<\/div><div class=\"spq_answer_block\" data-value=\"3\">5 units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 13 units<br\/>Volume of the cone $= 100\\pi$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$\\frac{1}{3} r^{2} h = 100\\pi$<br>\r\n$\\frac{1}{3} \\times r^{2} \\times 12 =100$<br>\r\n$4r^{2} = 100$<br>\r\n$r^{2} = \\frac{100}{4} = 25$<br>\r\n$r = 5$ units<br>\r\n$l = \\sqrt{r^{2} + h^{2}}$<br>\r\n$l = \\sqrt{5^{2} + 12^{2}} = \\sqrt{25 + 144}$<br>\r\n$l = \\sqrt{169} = 13$units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the volume of the right cone for the given radius 6 inches and height 14 inches? $( \\pi = 3.14)$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">507.52 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">527.52 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">537.29 cubic inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">507.51 cubic inches<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 527.52 cubic inches<br\/>Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $= \\frac{1}{3} \\pi r^{2} h$<br>\r\n$V =\\frac{1}{3} \\times 3.14 \\times 6 \\times 6 \\times 14 = 527.52$ cubic inches.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Volume of a Right Circular Cone \u2013 Definition, Formula, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Volume of a Right Circular Cone\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The slant height of the right circular cone is 13 inches and radius is 5 inches. What is the height of the cone?\",\n                    \"text\": \"The slant height of the right circular cone is 13 inches and radius is 5 inches. What is the height of the cone?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Radius (r) = 5 inches<br>\r\nSlant height (l) = 13 inches<br>\r\n$$h = \\\\sqrt{l^{2}\\\\;-\\\\;r^{2}}$$<br>\r\n$$h = \\\\sqrt{13^{2}\\\\;-\\\\;5^{2}} = \\\\sqrt{169\\\\;-\\\\;25} = \\\\sqrt{144} = 12$$ inches\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the volume of a right circular cone in terms of radius if radius is equal to the height.\",\n                    \"text\": \"Find the volume of a right circular cone in terms of radius if radius is equal to the height.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{3} \\\\pi r^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\pi r^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{3} \\\\pi r^{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{3} \\\\pi r^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let radius of the cone be r units and height of the cone be h units.<br>\r\nGiven: r = h<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} r = \\\\frac{1}{3} \\\\pi r^{3}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the height of the cone is 18 inches and base diameter is 14 inches, then what will be the volume of the cone?\",\n                    \"text\": \"If the height of the cone is 18 inches and base diameter is 14 inches, then what will be the volume of the cone?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1024 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"984 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"964 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"924 cubic inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base diameter of the cone (d)=14 inches<br>\r\nBase radius of the cone (r)=7 inches<br>\r\nHeight of the cone (h)=18 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$= \\\\frac{1}{3} \\\\times \\\\frac{22}{7} \\\\times 7 \\\\times 7 \\\\times 18 = 924$$ cubic inches.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the volume of the cone is 100 cubic units, and height is 12 units, then what will be the lateral height?\",\n                    \"text\": \"If the volume of the cone is 100 cubic units, and height is 12 units, then what will be the lateral height?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5 units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"13 units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of the cone $$= 100\\\\pi$$ cubic units<br>\r\nHeight of the cone (h) = 12 units<br>\r\n$$\\\\frac{1}{3} r^{2} h = 100\\\\pi$$<br>\r\n$$\\\\frac{1}{3} \\\\times r^{2} \\\\times 12 =100$$<br>\r\n$$4r^{2} = 100$$<br>\r\n$$r^{2} = \\\\frac{100}{4} = 25$$<br>\r\n$$r = 5$$ units<br>\r\n$$l = \\\\sqrt{r^{2} + h^{2}}$$<br>\r\n$$l = \\\\sqrt{5^{2} + 12^{2}} = \\\\sqrt{25 + 144}$$<br>\r\n$$l = \\\\sqrt{169} = 13$$units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the volume of the right cone for the given radius 6 inches and height 14 inches? $$( \\\\pi = 3.14)$$\",\n                    \"text\": \"What is the volume of the right cone for the given radius 6 inches and height 14 inches? $$( \\\\pi = 3.14)$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"507.52 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"537.29 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"507.51 cubic inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"527.52 cubic inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base radius of the cone (r) = 6 inches<br>\r\nHeight of the cone (h) =  14 inches<br>\r\nVolume of the cone $$= \\\\frac{1}{3} \\\\pi r^{2} h$$<br>\r\n$$V =\\\\frac{1}{3} \\\\times 3.14 \\\\times 6 \\\\times 6 \\\\times 14 = 527.52$$ cubic inches.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-volume-of-a-right-circular-cone\">Frequently Asked Questions about Volume of a Right Circular Cone<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\"><strong>What is the formula for curved surface area of a right circular cone?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\">\n\n<p>The formula for curved surface area of a right circular cone is $\\pi r l$, where r is the radius of the base and l is the slant height.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\"><strong>What is the total surface area of a right circular cone?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\">\n\n<p>The formula for total surface area of a right circular cone is $\\pi r l + r^{2} = r(l + r)$ where r is the radius of the base and l is the slant height.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\"><strong>What is an oblique circular cone?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\">\n\n<p>If the axis is not perpendicular to the base, the cone is called an oblique circular cone. In the oblique cone, the apex is not aligned with the center of the circular base<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\"><strong>If the radius and height of a right circular cone gets doubled, will the volume get doubled?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\">\n\n<p>Original volume $= \\frac{1}{3} \\pi r^{2} h$<\/p>\n\n\n\n<p>New Volume $= \\frac{1}{3} \\times (2r)^{2} \\times (2h) = 8 \\times \\frac{1}{3} \\pi r^{2}h = 8$ times original volume<\/p>\n\n\n\n<p>The volume gets 8 times the original volume.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\"><strong>How to find the volume of a layer of a right circular cone?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-8e8276fc-fa7c-46cf-8f8d-797e1e0412e8\">\n\n<p>To find the volume of a layer within a right circular cone, use the formula for the volume of a cone $(V = \\frac{1}{3} \\pi r^{2} h)$, where h and r represent the height and radius of the layer.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Volume of a Right Circular Cone? The volume of a right circular cone is the total space occupied by the right circular cone. It is equal to one-third the product of the base area and height. The formula to find the volume of a right circular cone is $V = \\frac{1}{3} \\pi &#8230; <a title=\"Volume of a Right Circular Cone \u2013 Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/volume-of-right-circular-cone\" aria-label=\"More on Volume of a Right Circular Cone \u2013 Definition, Formula, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-36059","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=36059"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36059\/revisions"}],"predecessor-version":[{"id":36081,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36059\/revisions\/36081"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}