{"id":234493,"date":"2025-06-14T07:34:20","date_gmt":"2025-06-14T07:34:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234493"},"modified":"2025-06-14T07:34:22","modified_gmt":"2025-06-14T07:34:22","slug":"the-volume-of-this-cone-is-100-48-cubic-centimeters","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/the-volume-of-this-cone-is-100-48-cubic-centimeters\/","title":{"rendered":"The volume of this cone is 100.48 cubic centimeters"},"content":{"rendered":"\n<p>The volume of this cone is 100.48 cubic centimeters. What is the height of this cone? Use<br>and round your answer to the nearest hundredth. 4 cm h<br>centimeters<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-481.png\" alt=\"\" class=\"wp-image-234494\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the height of the cone, one must use the formula for the volume of a cone: V = (1\/3)\u03c0r\u00b2h. In this formula, V stands for volume, \u03c0 (pi) is a mathematical constant, r represents the radius of the circular base, and h is the height of the cone.<\/p>\n\n\n\n<p>The problem provides the following values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The volume (V) is 100.48 cubic centimeters.<\/li>\n\n\n\n<li>The radius (r) of the cone&#8217;s base is 4 centimeters.<\/li>\n\n\n\n<li>The value to use for \u03c0 is approximately 3.14.<\/li>\n<\/ul>\n\n\n\n<p>The unknown variable to solve for is the height (h). The first step is to substitute the given values into the volume formula:<br>100.48 = (1\/3) \u00d7 3.14 \u00d7 (4)\u00b2 \u00d7 h<\/p>\n\n\n\n<p>Next, proceed with simplifying the equation. Start by calculating the square of the radius (r\u00b2):<br>4\u00b2 = 4 \u00d7 4 = 16<\/p>\n\n\n\n<p>Now, substitute this value back into the equation:<br>100.48 = (1\/3) \u00d7 3.14 \u00d7 16 \u00d7 h<\/p>\n\n\n\n<p>Then, multiply the numerical values on the right side of the equation:<br>3.14 \u00d7 16 = 50.24<\/p>\n\n\n\n<p>The equation now looks like this:<br>100.48 = (1\/3) \u00d7 50.24 \u00d7 h<\/p>\n\n\n\n<p>To solve for h, it&#8217;s necessary to isolate it. Begin by eliminating the fraction (1\/3). This is done by multiplying both sides of the equation by 3:<br>3 \u00d7 100.48 = 3 \u00d7 [(1\/3) \u00d7 50.24 \u00d7 h]<br>301.44 = 50.24 \u00d7 h<\/p>\n\n\n\n<p>The final step to find h is to divide both sides of the equation by 50.24:<br>h = 301.44 \/ 50.24<\/p>\n\n\n\n<p>Performing the division results in:<br>h = 6<\/p>\n\n\n\n<p>The problem asks for the answer to be rounded to the nearest hundredth. Since the calculated height is exactly 6, it can be written as 6.00 to meet this requirement.<\/p>\n\n\n\n<p>Thus, the height of the cone is approximately 6.00 centimeters.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-422.jpeg\" alt=\"\" class=\"wp-image-234495\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The volume of this cone is 100.48 cubic centimeters. What is the height of this cone? Useand round your answer to the nearest hundredth. 4 cm hcentimeters The Correct Answer and Explanation is: To find the height of the cone, one must use the formula for the volume of a cone: V = (1\/3)\u03c0r\u00b2h. In [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-234493","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234493","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=234493"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234493\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234493"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234493"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}