{"id":35302,"date":"2023-10-28T15:55:15","date_gmt":"2023-10-28T15:55:15","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35302"},"modified":"2023-10-29T18:22:53","modified_gmt":"2023-10-29T18:22:53","slug":"right-circular-cone-definition-properties-formulas-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone","title":{"rendered":"Right Circular Cone \u2013 Definition, Properties, Formulas, 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-bc91b3d0-0f93-4e09-bbf4-31c8336db302\" 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\/right-circular-cone#0-what-is-a-right-circular-cone>What Is a Right Circular Cone?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone#2-what-are-the-parts-of-a-right-circular-cone>What Are the Parts of a Right Circular Cone?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone#3-properties-of-right-circular-cone>Properties of Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone#12-solved-examples-on-right-circular-cone>Solved Examples on Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone#13-practice-problems-on-right-circular-cone>Practice Problems on Right Circular Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone#14-frequently-asked-questions-about-right-circular-cone>Frequently Asked Questions about Right Circular Cone<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-right-circular-cone\">What Is a Right Circular Cone?<\/h2>\n\n\n\n<p><strong>A right circular cone is a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/3-dimensional\"><strong>three-dimensional geometric shape<\/strong><\/a><strong> characterized by a circular base and a single curved surface that extends to a point called the apex or vertex. Its axis (the line joining the vertex and the center of the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/circle\"><strong>circle<\/strong><\/a><strong> at the base) is<\/strong><strong> perpendicular to the plane of the base.&nbsp;<\/strong><\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/cone\">cone<\/a> can be of two categories, depending upon the position of the axis: Right circular cone and oblique cone. The axis of the cone is the line that joins the vertex to the midpoint of the circular base.<\/p>\n\n\n\n<p>A right circular cone is one whose axis is <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/perpendicular\">perpendicular<\/a> to the base. Here, the axis makes a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-angle\">right angle<\/a>. A right circular cone is generated by a revolving right triangle about one of its legs.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"412\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-formed-by-revolving-a-right-triangle-about-its-leg-.png\" alt=\"Right circular cone formed by revolving a right triangle about its leg\u00a0\" class=\"wp-image-35309\" title=\"Right circular cone formed by revolving a right triangle about its leg\u00a0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-formed-by-revolving-a-right-triangle-about-its-leg-.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-formed-by-revolving-a-right-triangle-about-its-leg--300x200.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<p>In math, a cone is defined as a three-dimensional geometric figure with a flat base and curved surface pointed towards the top. The pointed end is the vertex, whereas the flat surface is called the base.<\/p>\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\/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\/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\/select-the-right-unit\" 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\/measurement_choose_right_unit_pt.png\" alt=\"Select the Right Unit 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\">Select the Right Unit 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-right-circular-cone-definition\">Right Circular Cone: Definition<\/h2>\n\n\n\n<p><strong>A right circular cone is a type of cone whose axis is perpendicular to the flat circular base.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone.png\" alt=\"right circular cone\" class=\"wp-image-35310\" title=\"right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-what-are-the-parts-of-a-right-circular-cone\">What Are the Parts of a Right Circular Cone?<\/h2>\n\n\n\n<p>Let\u2019s learn about the important parts or elements of a right circular cone.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex of a Right Circular Cone<\/strong>: The flat circular base and the curved surface of a cone smoothly narrows down to a point called \u201c<a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/vertex\">vertex<\/a>\u201d or \u201capex.\u201d<\/li>\n\n\n\n<li><strong>Base of a Right Circular Cone<\/strong>: The base of a right circular cone is a circle.<\/li>\n\n\n\n<li><strong>Radius of a Right Circular Cone<\/strong>: It is the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/radius-of-a-circle\">radius of the circle<\/a> at its base.<\/li>\n\n\n\n<li><strong>Axis\/Height of a Right Circular Cone:<\/strong> The fixed line which joins the vertex and center of the base is called the axis\/<a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/height\">height<\/a> of the cone.<\/li>\n\n\n\n<li><strong>Slant Height of a Right Circular Cone:<\/strong> The length of the line joining the vertex to any point on the circular edge of the base is called slant height. Generally, It is denoted by \u201cl.\u201d<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"692\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-a-right-circular-cone.png\" alt=\"Parts of a right circular cone\" class=\"wp-image-35312\" title=\"Parts of a right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-a-right-circular-cone.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/parts-of-a-right-circular-cone-269x300.png 269w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-properties-of-right-circular-cone\">Properties of Right Circular Cone<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>It has one circular base.<\/li>\n\n\n\n<li>It has one vertex (apex).<\/li>\n\n\n\n<li>It has one curved edge.<\/li>\n\n\n\n<li>Slant height of the right circular cone is the line joining the vertex to any point on the circular edge of the base.<\/li>\n\n\n\n<li>A right circular cone is created by rotating a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\">right triangle<\/a> with the perpendicular side as the axis of rotation.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-right-circular-cone-formulas\">Right Circular Cone Formulas<\/h2>\n\n\n\n<p>Consider a right circular cone with radius \u201cr,\u201d height \u201ch,\u201d and slant height &#8220;l.\u201d<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Relationship between slant height, height, and radius: l<sup>2<\/sup> = h<sup>2<\/sup> + r<sup>2<\/sup><\/li>\n\n\n\n<li>Curved surface area of right circular cone = \u03c0 r l<\/li>\n\n\n\n<li>Total surface area of a right circular cone = \u03c0r(r + l)<\/li>\n\n\n\n<li>Volume of a right circular cone $= \\frac{1}{3} \\pi r^{2} h$<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"503\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-with-base-radius-r-height-h-and-slant-height-l.png\" alt=\"Right circular cone with base radius r, height h, and slant height l\" class=\"wp-image-35313\" title=\"Right circular cone with base radius r, height h, and slant height l\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-with-base-radius-r-height-h-and-slant-height-l.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-with-base-radius-r-height-h-and-slant-height-l-300x243.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-surface-area-of-a-right-circular-cone\">Surface Area of a Right Circular Cone<\/h2>\n\n\n\n<p>The surface area of a three-dimensional shape is the sum of all of the surface areas of each of the sides. A right circular cone has two surface areas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Lateral surface area\/Curved surface area<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The lateral surface area\/curved surface area is the surface of the cone excluding the flat circular base.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/lateral-surface-area-of-right-circular-cone.png\" alt=\"Lateral surface area of right circular cone\" class=\"wp-image-35314\" title=\"Lateral surface area of right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/lateral-surface-area-of-right-circular-cone.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/lateral-surface-area-of-right-circular-cone-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, \u201ch\u201d&nbsp;is the height, \u201cl\u201d is the slant height, \u201cc\u201d is the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/circumference-of-a-circle\">circumference<\/a> of the base, and&nbsp;\u201dr\u201d&nbsp;is the radius of the base. If we unroll it, the shape is as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"361\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/sector-of-a-circle-with-a-radius-l-and-arc-length-2\u03c0r.png\" alt=\"Sector of a circle with a radius \u201cl\u201d and arc length \u201c2\u03c0r\u201d\" class=\"wp-image-35315\" title=\"Sector of a circle with a radius \u201cl\u201d and arc length \u201c2\u03c0r\u201d\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/sector-of-a-circle-with-a-radius-l-and-arc-length-2\u03c0r.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/sector-of-a-circle-with-a-radius-l-and-arc-length-2\u03c0r-300x175.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<p>It is a&nbsp;sector of a circle&nbsp;with a radius&nbsp;\u201dl\u201d&nbsp;and arc length \u201cc.\u201d So, the curved surface area of the cone is equal to the area of the above sector having radius <em>l<\/em>. The area of a sector given the arc length&nbsp;\u201dc\u201d&nbsp;and radius &#8220;l&#8221;&nbsp;is given by,<\/p>\n\n\n\n<p>\u00a0\u2234 Curved surface area = Area of sector $=\u00a0\\frac{1}{2} \\times 2\\pi rl = \\pi rl$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Total Surface Area of a Right Circular Cone<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The lateral surface area plus the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone\">base area of the cone<\/a> is equal to the total surface area.<\/p>\n\n\n\n<p>Total surface area = Curved surface area + Area of circular base<\/p>\n\n\n\n<p>= \u03c0rl + \u03c0r<sup>2<\/sup><\/p>\n\n\n\n<p>= \u03c0r(l + r )<\/p>\n\n\n\n<p>\u2234 Total surface area =\u03c0r(l + r )<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-volume-of-a-right-circular-cone\">Volume of a Right Circular Cone<\/h2>\n\n\n\n<p>If a right circular cone has radius \u201cr\u201d and height \u201ch,\u201d then its <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/volume\">volume<\/a> is equal to the one-third of&nbsp;<\/p>\n\n\n\n<p>the product of the area of the circular base and its height. Let\u2019s understand how to find the volume of a right circular cone.<\/p>\n\n\n\n<p><strong>Volume of right circular cone formula:<\/strong><\/p>\n\n\n\n<p>Volume of a right circular cone $= \\frac{1}{3} \\times $(base area)$\\times$ height $= \\frac{1}{3} \\pi r^{2} \\times h$<\/p>\n\n\n\n<p>Volume of a right circular cone $= \\frac{1}{3} \\times \\pi r^{2} \\times h = \\frac{1}{3} \\pi r^{2}h$<\/p>\n\n\n\n<p>Volume is measured in cubic units.<\/p>\n\n\n\n<p><strong>Volume of a right circular cone using diameter: We know that <\/strong>$r = \\frac{d}{2}$.<\/p>\n\n\n\n<p>Volume of a right circular cone $= \\frac{1}{12} \\pi d^{2}h$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frustum-of-a-right-circular-cone\">Frustum of a Right Circular Cone<\/h2>\n\n\n\n<p>When a right circular cone is cut off by a plane parallel to its base, a frustum forms in the area between the base and the parallel plane. And the upper part remains in the same shape as the right circular cone.<\/p>\n\n\n\n<p>The lower part is called the frustum of a right circular cone.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"345\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/frustum-of-a-right-circular-cone.png\" alt=\"Frustum of a right circular cone\" class=\"wp-image-35316\" title=\"Frustum of a right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/frustum-of-a-right-circular-cone.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/frustum-of-a-right-circular-cone-300x167.png 300w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-right-circular-cone-vs-oblique-cone\">Right Circular Cone vs. Oblique Cone<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A right circular cone or a regular cone has its axis perpendicular to its base. The axis joins the vertex to the center of the base.&nbsp;<\/li>\n\n\n\n<li>If the vertex position is not over the center of the base, it is an oblique cone. Here, the axis is non-perpendicular.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"342\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-v-oblique-cone.png\" alt=\"Right circular cone v. oblique cone\" class=\"wp-image-35317\" title=\"Right circular cone v. oblique cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-v-oblique-cone.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-v-oblique-cone-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-real-life-examples-of-a-right-circular-cone\">Real-life Examples of a Right Circular Cone<\/h2>\n\n\n\n<p>In our daily life, we come across many objects with conical shapes, such as an ice cream cone, a traffic cone, or a birthday hat.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-examples-of-cones.png\" alt=\"Real-life examples of cones\" class=\"wp-image-35318\" title=\"Real-life examples of cones\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-examples-of-cones.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/real-life-examples-of-cones-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-facts-about-right-circular-cone\">Facts about 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 cone and pyramid are closely related geometric shapes, and interestingly, their surface area formulas share similarities.<\/li>\n\n\n\n<li>Right circular cones have rotational symmetry, which means they may be rotated around their axis while maintaining their appearance.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the right circular cone, its parts, properties, and formulas for finding the surface area and volume. We also learned about the frustum of a right circular cone, and some fun facts. Let\u2019s solve a few examples and practice MCQs based on the learned concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-on-right-circular-cone\">Solved Examples on Right Circular Cone<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find the radius of a right circular cone whose slant height is 15 feet and height is 9 feet.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>l = 15 feet, and h = 9 feet.<\/p>\n\n\n\n<p>Since, l<sup>2<\/sup> = h<sup>2<\/sup> + r<sup>2<\/sup><\/p>\n\n\n\n<p>15<sup>2<\/sup> = 9<sup>2<\/sup> + r<sup>2<\/sup><\/p>\n\n\n\n<p>225 = 81 + r<sup>2<\/sup><\/p>\n\n\n\n<p>r<sup>2<\/sup> = 144<\/p>\n\n\n\n<p>$r = \\sqrt{144} = 12$<\/p>\n\n\n\n<p>Hence, the radius of the given right circular cone is 12 feet.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>A cone has a circular base of radius 8 units and a height of 15 units.&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Calculate (i) Lateral surface area and (ii) Total surface area.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"319\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-.png\" alt=\"Right circular cone\" class=\"wp-image-35319\" title=\"Right circular cone\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone-.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/right-circular-cone--282x300.png 282w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>Radius of circular base (r) = 8 units<\/p>\n\n\n\n<p>Height of cone (h) = 15 units<\/p>\n\n\n\n<p>Let\u2019s calculate the slant height (l).<\/p>\n\n\n\n<p>l<sup>2<\/sup> = h<sup>2<\/sup> + r<sup>2<\/sup><\/p>\n\n\n\n<p>l<sup>2<\/sup> = 82 + 15<sup>2<\/sup><\/p>\n\n\n\n<p>l<sup>2<\/sup> = 64 + 225<\/p>\n\n\n\n<p>l<sup>2<\/sup> = 289 \u00a0 \u00a0 \u00a0<\/p>\n\n\n\n<p>\u2234 l $= \\sqrt{289} = 17$ units<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lateral surface area = \u03c0rl = 3.14 \u00d7 8 \u00d7 17\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Lateral surface area = 427.04 units<sup>2<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total surface area = \u03c0r(l + r)<\/li>\n<\/ul>\n\n\n\n<p>Total surface area = 3.14 \u00d7 8 \u00d7 (17 + 8)<\/p>\n\n\n\n<p>Total surface area = 3.148 \u00d7 25<\/p>\n\n\n\n<p>Total surface area = 628 units<sup>2<\/sup><\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>Find the volume of a right circular cone with a radius of 21 in and a height of 5 in.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Radius (r) = 21 in<\/p>\n\n\n\n<p>Height (h) = 5 in<\/p>\n\n\n\n<p>We know that volume of a right circular cone $= \\frac{1}{3} \\pi r^{2}h$<\/p>\n\n\n\n<p>$V = \\frac{1}{3} \\times \\frac{22}{7} \\times 21^{2} \\times 5$<\/p>\n\n\n\n<p>$V = \\frac{1}{3} \\times \\frac{22}{7} \\times 21^{2} \\times 5 = 6930$ in<sup>3<\/sup><\/p>\n\n\n\n<p>Hence, the volume of the given cone is 6930 in<sup>3<\/sup>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-right-circular-cone\">Practice Problems on Right Circular Cone<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Right Circular Cone \u2013 Definition, Properties, Formulas, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following are parts of a right circular cone?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Radius<\/div><div class=\"spq_answer_block\" data-value=\"1\">Height<\/div><div class=\"spq_answer_block\" data-value=\"2\">Slant height<\/div><div class=\"spq_answer_block\" data-value=\"3\">All of the above<\/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: All of the above<br\/>Radius, height, and slant height is the part of a right circular cone.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the total surface area of a right circular cone of radius r and slant height l?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">r(l + r)<\/div><div class=\"spq_answer_block\" data-value=\"1\">\u03c0rl<\/div><div class=\"spq_answer_block\" data-value=\"2\">\u03c0r(l + r)<\/div><div class=\"spq_answer_block\" data-value=\"3\">2\u03c0r(l + r)<\/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: \u03c0r(l + r)<br\/>The total surface area of a right circular cone of radius r and slant height l is given by \u03c0r(l + r).<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If a right circular cone has a base radius of 4 inches and a height of 3 inches, then what is its slant height?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3 inches<\/div><div class=\"spq_answer_block\" data-value=\"1\">4 inches<\/div><div class=\"spq_answer_block\" data-value=\"2\">5 inches<\/div><div class=\"spq_answer_block\" data-value=\"3\">6 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: 5 inches<br\/>Slant height is given by: $l^{2} = h^{2} + r^{2}$<br>\r\n$l^{2} = 3^{2} + 4^{2} = 25$<br>\r\nTherefore, l = 5 inches<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The volume of a right circular cone is equal to one-third of the product of the area of the _____ and its height.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Cone<\/div><div class=\"spq_answer_block\" data-value=\"1\">Circular base<\/div><div class=\"spq_answer_block\" data-value=\"2\">Curved surface area<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: Circular base<br\/>The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the ______ of the cone.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Height<\/div><div class=\"spq_answer_block\" data-value=\"1\">Slant height<\/div><div class=\"spq_answer_block\" data-value=\"2\">Base<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: Base<br\/>The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.<\/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\": \"Right Circular Cone \u2013 Definition, Properties, Formulas, Examples\",        \n        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   \"@type\": \"Comment\",\n                        \"text\": \"Radius, height, and slant height is the part of a right circular cone.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the total surface area of a right circular cone of radius r and slant height l?\",\n                    \"text\": \"What is the total surface area of a right circular cone of radius r and slant height l?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The total surface area of a right circular cone of radius r and slant height l is given by \u03c0r(l + r).\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"r(l + r)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The total surface area of a right circular cone of radius r and slant height l is given by \u03c0r(l + r).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u03c0rl\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The total surface area of a right circular cone of radius r and slant height l is given by \u03c0r(l + r).\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\u03c0r(l + r)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The total surface area of a right circular cone of radius r and slant height l is given by \u03c0r(l + r).\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"\u03c0r(l + r)\",\n                      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inches, then what is its slant height?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6 inches\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5 inches\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Slant height is given by: $$l^{2} = h^{2} + r^{2}$$<br>\r\n$$l^{2} = 3^{2} + 4^{2} = 25$$<br>\r\nTherefore, l = 5 inches\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The volume of a right circular cone is equal to one-third of the product of the area of the _____ and its height.\",\n                    \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the _____ and its height.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Cone\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Curved surface area\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Circular base\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The volume of a right circular cone is equal to one-third of the product of the area of the circular base and its height.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the ______ of the cone.\",\n                    \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the ______ of the cone.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Height\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Slant height\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Base\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The frustum of a cone is formed when a right circular cone is cut by a plane that is parallel to the \u201cbase\u201d of the cone.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-about-right-circular-cone\">Frequently Asked Questions about Right Circular Cone<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" 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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>How many edges and vertices does a right circular cone have?<\/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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>A right circular cone has one curved edge and one vertex. The pointed vertex at the top of the cone is also called \u201capex.\u201d<\/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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>Is the right circular cone a polyhedron?<\/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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>No, the right circular cone is not a polyhedron. Polyhedrons are three-dimensional geometric shapes with flat, polygonal faces. A cone, including the right circular cone, has curved, non-polygonal surfaces and a single curved face, making it distinct from polyhedra.<\/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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>What is the difference between a right circular cone and a 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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>The apex of a right circular cone is positioned directly above the center of its base. This alignment results in a line that runs from the apex to the base&#8217;s center, forming a right angle with the cone&#8217;s radius. In contrast, for a general cone, the apex can be located at any point.<\/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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>How do you find the slant height 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-3-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>The slant height of a right circular cone can be determined using the formula $l^{2} = h^{2} +  r^{2}$.Where, r = radius, h = height, and l= 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-4-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>What is the formula for finding the surface areas 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-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>(i) Curved surface area of right circular cone = \u03c0 r l<\/p>\n\n\n\n<p>(ii) Total surface area of a right circular cone = \u03c0r(r + l)\u00a0<\/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-5-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\"><strong>How do you find the volume of a cone if radius and slant height are given?<\/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-5-ac5bb19e-e94e-4a0b-93c8-a52d98a3ff20\">\n\n<p>If the radius(r) and slant height(l) of a cone is given, then first find the height of the cone. Then apply the formula: Volume of a right circular cone $= \\frac{1}{3}\u03c0r^{2} h$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Right Circular Cone? A right circular cone is a three-dimensional geometric shape characterized by a circular base and a single curved surface that extends to a point called the apex or vertex. Its axis (the line joining the vertex and the center of the circle at the base) is perpendicular to the &#8230; <a title=\"Right Circular Cone \u2013 Definition, Properties, Formulas, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/right-circular-cone\" aria-label=\"More on Right Circular Cone \u2013 Definition, Properties, Formulas, 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-35302","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\/35302","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=35302"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35302\/revisions"}],"predecessor-version":[{"id":35324,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35302\/revisions\/35324"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}