{"id":34760,"date":"2023-10-07T07:30:37","date_gmt":"2023-10-07T07:30:37","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34760"},"modified":"2023-10-11T10:07:20","modified_gmt":"2023-10-11T10:07:20","slug":"base-area-of-a-cone-definition-formula-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone","title":{"rendered":"Base Area of a Cone &#8211; Definition, Formula, Examples, Facts, FAQs"},"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-fc7e962d-3b4e-49c8-aaff-d0010ad0aca3\" 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\/base-area-of-a-cone#0-what-is-the-base-area-of-a-cone>What Is the Base Area of a Cone?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone#1-base-area-of-a-cone-formula>Base Area of a Cone Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone#2-how-to-find-the-base-area-of-a-cone>How to Find the Base Area of a Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone#5-solved-examples-on-the-base-area-of-a-cone>Solved Examples on the Base Area of a Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone#6-practice-problems-on-the-base-area-of-a-cone>Practice Problems on the Base Area of a Cone<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone#7-frequently-asked-questions-about-the-base-area-of-a-cone>Frequently Asked Questions about the Base Area of a Cone<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-base-area-of-a-cone\">What Is the Base Area of a Cone?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The surface area of a cone&#8217;s circular base is referred to as its base area.<\/strong> <strong>It is simply the area of the base of a cone.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/cone\">cone<\/a> is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/3-dimensional\">three-dimensional geometric shape<\/a> with a circular base and a curved surface that narrows down to a single point known as the apex or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/vertex\">vertex<\/a>. The base area is crucial in defining the cone&#8217;s total surface area and volume.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Before moving on to calculating the base area of a cone, it is important to recall the basics.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Parts of a Cone:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are three parts of a cone. They are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Base: The flat circular surface at a cone&#8217;s bottom face.<\/li>\n\n\n\n<li>Apex (Vertex): The apex is the pointed tip of a cone where all of its slanted sides converge.<\/li>\n\n\n\n<li>Lateral Surface: The curved surface that joins the base with the apex.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Dimensions of a Cone<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Height of a Cone: The vertical distance from the apex to the base.<\/li>\n\n\n\n<li>Slant Height of a Cone: The distance from the apex to any point on the circular edge.<\/li>\n\n\n\n<li>Radius of the Base of a Cone: The distance from the center of the circular base to its edge.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"322\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/surfaces-and-dimensions.png\" alt=\"surfaces and dimensions\" class=\"wp-image-34765\" title=\"surfaces and dimensions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/surfaces-and-dimensions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/surfaces-and-dimensions-300x156.png 300w\" 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\/add-multiples-of-100-using-base-10-blocks\" 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\/add_sub_pv_add_multiples_100_model_pt.png\" alt=\"Add Multiples of 100 Using Base-10 Blocks 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\">Add Multiples of 100 Using Base-10 Blocks 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\/add-to-find-the-area\" 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_find_area_pt.png\" alt=\"Add to Find the Area 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\">Add to Find the Area 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\/add-using-base-10-blocks\" 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\/add_sub_pv_add_2d_2d_model_pt.png\" alt=\"Add Using Base-10 blocks 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\">Add Using Base-10 blocks 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\/area-of-composite-figure\" 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_grannys_rescue_10_gm.png\" alt=\"Area of Composite Figure 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\">Area of Composite Figure 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\/area-with-unit-squares-and-side-lengths\" 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_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths 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\">Area with Unit Squares and Side Lengths 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\/area-word-problems-on-product-of-fractions\" 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\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions 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\">Area Word Problems on Product of Fractions 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\/build-the-area\" 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_grannys_rescue_3_4_5_gm.png\" alt=\"Build the Area 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\">Build the Area 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\/choose-the-equivalent-value-based-on-place-value\" 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\/place_value_relate_value_diff_places_pt.png\" alt=\"Choose the Equivalent Value Based on Place Value 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\">Choose the Equivalent Value Based on Place Value 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\/compose-numbers-based-on-tens-and-ones\" 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\/place_value_compose_10s_1s_1_pt.png\" alt=\"Compose Numbers based on Tens and Ones 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\">Compose Numbers based on Tens and Ones 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\/count-in-tens-using-base-10-blocks\" 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\/place_value_count_10s_base_10_block_pt.png\" alt=\"Count in Tens using Base 10 Blocks 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\">Count in Tens using Base 10 Blocks 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-base-area-of-a-cone-formula\">Base Area of a Cone Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for calculating the base area of a cone is obtained from the area of a circle. Since a cone&#8217;s base is a circle, we can calculate its base area using the method for calculating the area of a circle:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Base Area (A) <\/strong>$= \\pi \\times r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A denotes the base area of the cone<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03c0 (pi) is a mathematical constant approximately equal to 3.14159<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">r denotes the radius of the circular base 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\/add-fractions-using-area-models\" 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\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" 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\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" 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\/add-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and Fractions using Area Models 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-multiples-of-10-using-base-10-blocks\" 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\/add-multiples-of-10-using-base-10-blocks.jpeg\" alt=\"Add Multiples of 10 using Base 10 Blocks 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-fractions-using-area-model\" 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\/compare-fractions-using-area-model.jpeg\" alt=\"Compare Fractions Using Area Model 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-using-base-10-blocks\" 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\/compare-using-base-10-blocks.jpeg\" alt=\"Compare Using Base-10 Blocks 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-area-model\" 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\/complete-the-area-model.jpeg\" alt=\"Complete the Area Model 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-the-equation-for-the-area-model\" 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\/complete-the-equation-for-the-area-model.jpeg\" alt=\"Complete the Equation for the Area Model 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 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/convert-mixed-numbers-using-area-models\" 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\/convert-mixed-numbers-using-area-models.jpeg\" alt=\"Convert Mixed Numbers Using Area Models 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-base-area-of-a-cone\">How to Find the Base Area of a Cone<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Follow the steps given below to find the base area of a cone:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Note down the radius (r) of the circular base, which is the distance from the circle&#8217;s center to any point on its edge.<\/li>\n\n\n\n<li>Put the values in the formula for the base area.<br><br>$A = \\pi \\times r^{2}$<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify and assign the unit \u201csquare units\u201d depending on the unit of the radius.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: <\/strong>If a cone has a radius of its circular base to be 5 units, then what will be the base area of the cone?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times (5^{2}) = 25\\pi$ square units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-the-base-area-of-a-cone\">Facts about the Base Area of a 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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The base area of a cone increases as the radius of the circular base increases.<\/li>\n\n\n\n<li>The cone has the largest base area among all three-dimensional shapes with a fixed volume.&nbsp;<\/li>\n\n\n\n<li>Total Surface Area of a Cone = Base Area + Curved Surface Area<\/li>\n\n\n\n<li>Volume of a Cone $= \\frac{1}{3} \\times$Base Area $\\times$ Height $= \\frac{1}{3}\\pi r^{2}h$<\/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 class=\"wp-block-paragraph\">In this article, we learned about the base area of a cone, which is represented by \u03c0r<sup>2<\/sup>, where r is the radius of the circular base of the cone. Understanding this fundamental concept is essential for calculating the cone&#8217;s volume and surface area. Let&#8217;s solve a few examples and practice MCQs for better comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-the-base-area-of-a-cone\">Solved Examples on the Base Area of a Cone<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1: Calculate the base area of a 4-unit-radius cone.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Radius (r) = 4 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Use the formula for the base area of a cone.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times (4 \\;units)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times 16\\; units^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = 50.27\\; units^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the base area of the cone is 50.27 square units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2: A traffic cone has a radius of the base 7 inches. Find the base area of the cone.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Radius (r) = 7 inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Use the formula for the base area of a cone to find the base area of the traffic cone.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On substituting the value of the radius into the formula, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi (7\\; inches)^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = \\pi \\times 49$ square inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = 3.14 \\times 49$ square inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$A = 153.86$ square inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the base area of the traffic cone is 153.86 square inches.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 3: A cone&#8217;s circular base has to be covered with marble, and its base area is 36 square feet. What is the total cost to cover the entire base if the cost of marble is $5 per square foot?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total Cost = Base Area $\\times$ Cost per square foot<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total Cost $= 36 \\times \\$5$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total Cost $= \\$180$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 4: Find the radius of a cone that has a base area of 100 square units<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area (A) = 100 square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area $(A) = \\pi \\times r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the value of the base area in the formula, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$100 = \\pi \\times r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let us divide both sides of the equation by \u03c0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r^{2} = \\frac{100}{\\pi}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take the square root of both sides.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r = \\sqrt{\\frac{100}{\\pi}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r = \\sqrt{31.83098862}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r = 5.64$ units (rounded to two decimal places)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the cone radius is about 5.64 units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 5: Find the radius of the cone whose base area is 36\u03c0 square meters.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area $(A) = 36\\pi$ square units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On applying the formula, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area $(A) = \\pi r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$36\\pi = \\pi r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Divide both sides of the equation by \u03c0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r^{2} = 36$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take the square root of both sides.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r = \\sqrt{36}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$r = 6$ units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the radius of the cone is 6 units.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-the-base-area-of-a-cone\">Practice Problems on the Base Area of a Cone<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Base Area of a Cone - Definition, Formula, Examples, Facts, FAQs<\/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\">What is the formula for computing the base area of a cone?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$A = \\pi r^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$A = 2\\pi r$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$A = 4\\pi r^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$A = 0.5\\pi r^{2}$<\/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: $A = \\pi r^{2}$<br\/>Base area of a cone $= \\pi r^{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the base area of a cone whose base has the radius of 10 units?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">100 square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">50\u03c0 square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">100\u03c0 square units<\/div><div class=\"spq_answer_block\" data-value=\"3\">314 square 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: 100 square units<br\/>$A = \\pi r^{2}$\r\n$A = \\pi \\times (10)^{2} = 100\\pi \\;unit^{2}$<\/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\">Volume of a cone =<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(Base\\; Area)^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$Base \\;Area \\times Height$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{2} \\times Base \\;Area \\times Height$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{3} \\times Base \\;Area \\times Height$<\/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: $\\frac{1}{3} \\times Base \\;Area \\times Height$<br\/>Volume of a cone $= \\frac{1}{3} \\times Base \\;Area \\times Height$<\/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\": \"Base Area of a Cone - Definition, Formula, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Base Area of a Cone\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the formula for computing the base area of a cone?\",\n                    \"text\": \"What is the formula for computing the base area of a cone?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A = 2\\\\pi r$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A = 4\\\\pi r^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$A = 0.5\\\\pi r^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$A = \\\\pi r^{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base area of a cone $$= \\\\pi r^{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the base area of a cone whose base has the radius of 10 units?\",\n                    \"text\": \"What is the base area of a cone whose base has the radius of 10 units?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50\u03c0 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100\u03c0 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"314 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"100 square units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$A = \\\\pi r^{2}$$\r\n$$A = \\\\pi \\\\times (10)^{2} = 100\\\\pi \\\\;unit^{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Volume of a cone =\",\n                    \"text\": \"Volume of a cone =\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(Base\\\\; Area)^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$Base \\\\;Area \\\\times Height$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2} \\\\times Base \\\\;Area \\\\times Height$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Volume of a cone $$= \\\\frac{1}{3} \\\\times Base \\\\;Area \\\\times Height$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-the-base-area-of-a-cone\">Frequently Asked Questions about the Base Area of a Cone<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-ee33c061-dc93-4ee5-a5ed-25f8535974fe\" 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-ee33c061-dc93-4ee5-a5ed-25f8535974fe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee33c061-dc93-4ee5-a5ed-25f8535974fe\"><strong>What happens to the base area of a cone if the radius of the base is 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-0-ee33c061-dc93-4ee5-a5ed-25f8535974fe\">\n\n<p class=\"wp-block-paragraph\">When the radius of a cone&#8217;s base is doubled, the base area of the cone grows four times.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Base Area (A) $= \\pi r^{2}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the new radius be &#8220;2r.&#8221;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the new base area $= \\pi \\times (2r)^{2} = \\pi 4r^{2} = 4(\\pi \\times r^{2})$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, the new base area grows four times the original base area by doubling the radius.<\/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-ee33c061-dc93-4ee5-a5ed-25f8535974fe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee33c061-dc93-4ee5-a5ed-25f8535974fe\"><strong>How is the base area of a cone related to its slant height?<\/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-ee33c061-dc93-4ee5-a5ed-25f8535974fe\">\n\n<p class=\"wp-block-paragraph\">The base area is not directly related to the slant height; it only depends on the radius.<\/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-ee33c061-dc93-4ee5-a5ed-25f8535974fe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ee33c061-dc93-4ee5-a5ed-25f8535974fe\"><strong>Is the base area the same as the lateral surface area?<\/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-ee33c061-dc93-4ee5-a5ed-25f8535974fe\">\n\n<p class=\"wp-block-paragraph\">No, the base area is separate from the lateral surface area of a cone. Lateral surface area is simply the curved surface area of the cone.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Base Area of a Cone? The surface area of a cone&#8217;s circular base is referred to as its base area. It is simply the area of the base of a cone. A cone is a three-dimensional geometric shape with a circular base and a curved surface that narrows down to a single &#8230; <a title=\"Base Area of a Cone &#8211; Definition, Formula, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/base-area-of-a-cone\" aria-label=\"More on Base Area of a Cone &#8211; Definition, Formula, Examples, Facts, FAQs\">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-34760","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\/34760","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=34760"}],"version-history":[{"count":6,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34760\/revisions"}],"predecessor-version":[{"id":34772,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34760\/revisions\/34772"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34760"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34760"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}