{"id":232545,"date":"2025-06-12T02:37:33","date_gmt":"2025-06-12T02:37:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232545"},"modified":"2025-06-12T02:37:35","modified_gmt":"2025-06-12T02:37:35","slug":"kerry-bought-a-conical-tent-to-put-on-the-back-porch","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/kerry-bought-a-conical-tent-to-put-on-the-back-porch\/","title":{"rendered":"Kerry bought a conical tent to put on the back porch"},"content":{"rendered":"\n<p>. The tent instructions reveal the height at the tallest point to be 4.5 feet and the space inside to be 10.5 cubic feet. About how many square feet of the back porch will be covered by the tent? Which measure of the cone needs to be calculated to answer the problem? A. diameter B. Radius C. Base area D. Volume. Which equation represents the scenario? A. V = (1\/3)(10.5)(4.5) B. 4.5 = (1\/3)(10.5)(h) C. 10.5 = (1\/3)(4.5)(h) D. 10.5 = (1\/3)(B)(4.5). How many square feet of the back porch will the tent cover? A. 2.33 square feet B. 6 square feet C. 7 square feet D. 15.75 square feet.<\/p>\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>We use the <strong>volume formula for a cone<\/strong>:V=13\u03c0r2hV = \\frac{1}{3} \\pi r^2 hV=31\u200b\u03c0r2h<\/p>\n\n\n\n<p>We are given V=10.5V = 10.5V=10.5 and h=4.5h = 4.5h=4.5, and we need to solve for rrr, which helps us find the base area.<\/p>\n\n\n\n<p>Let\u2019s substitute the known values into the formula:10.5=13\u03c0r2(4.5)10.5 = \\frac{1}{3} \\pi r^2 (4.5)10.5=31\u200b\u03c0r2(4.5)<\/p>\n\n\n\n<p>Simplify:10.5=4.53\u03c0r2=1.5\u03c0r210.5 = \\frac{4.5}{3} \\pi r^2 = 1.5 \\pi r^210.5=34.5\u200b\u03c0r2=1.5\u03c0r2<\/p>\n\n\n\n<p>Now divide both sides by 1.5\u03c01.5\\pi1.5\u03c0:r2=10.51.5\u03c0=10.54.71238898\u22482.23r^2 = \\frac{10.5}{1.5\\pi} = \\frac{10.5}{4.71238898} \\approx 2.23r2=1.5\u03c010.5\u200b=4.7123889810.5\u200b\u22482.23<\/p>\n\n\n\n<p>Then:r\u22482.23\u22481.49&nbsp;feetr \\approx \\sqrt{2.23} \\approx 1.49 \\text{ feet}r\u22482.23\u200b\u22481.49&nbsp;feet<\/p>\n\n\n\n<p>Now we find the <strong>base area<\/strong> using:A=\u03c0r2\u2248\u03c0(1.49)2\u22483.14\u00d72.23\u22487.0&nbsp;square&nbsp;feetA = \\pi r^2 \\approx \\pi (1.49)^2 \\approx 3.14 \\times 2.23 \\approx 7.0 \\text{ square feet}A=\u03c0r2\u2248\u03c0(1.49)2\u22483.14\u00d72.23\u22487.0&nbsp;square&nbsp;feet<\/p>\n\n\n\n<p>So, the <strong>area of the base<\/strong>, or how much of the back porch the tent covers, is about <strong>7 square feet<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Correct Answers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Which measure?<\/strong> \u2192 <strong>C. Base area<\/strong><\/li>\n\n\n\n<li><strong>Which equation?<\/strong> \u2192 <strong>D. 10.5=13B\u22c54.510.5 = \\frac{1}{3} B \\cdot 4.510.5=31\u200bB\u22c54.5<\/strong><\/li>\n\n\n\n<li><strong>Area of porch covered?<\/strong> \u2192 <strong>C. 7 square feet<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>To find how much space the conical tent covers on the porch, we need to determine the area of the base of the cone, since that is the part in contact with the porch. A cone\u2019s base is a circle, and the area of a circle is given by the formula A=\u03c0r2A = \\pi r^2A=\u03c0r2, where rrr is the radius.<\/p>\n\n\n\n<p>However, we are not given the radius directly. Instead, we are given the volume of the cone (10.5 cubic feet) and the height (4.5 feet). We use the formula for the volume of a cone to find the missing radius:V=13\u03c0r2hV = \\frac{1}{3} \\pi r^2 hV=31\u200b\u03c0r2h<\/p>\n\n\n\n<p>Substituting the known values into the formula, we get:10.5=13\u03c0r2\u22c54.510.5 = \\frac{1}{3} \\pi r^2 \\cdot 4.510.5=31\u200b\u03c0r2\u22c54.510.5=1.5\u03c0r210.5 = 1.5 \\pi r^210.5=1.5\u03c0r2<\/p>\n\n\n\n<p>Now solve for r2r^2r2:r2=10.51.5\u03c0\u224810.54.71\u22482.23r^2 = \\frac{10.5}{1.5\\pi} \\approx \\frac{10.5}{4.71} \\approx 2.23r2=1.5\u03c010.5\u200b\u22484.7110.5\u200b\u22482.23r\u22482.23\u22481.49&nbsp;feetr \\approx \\sqrt{2.23} \\approx 1.49 \\text{ feet}r\u22482.23\u200b\u22481.49&nbsp;feet<\/p>\n\n\n\n<p>Finally, we plug the radius back into the area formula:A=\u03c0r2\u22483.14\u00d72.23\u22487.0A = \\pi r^2 \\approx 3.14 \\times 2.23 \\approx 7.0A=\u03c0r2\u22483.14\u00d72.23\u22487.0<\/p>\n\n\n\n<p>So, the tent covers about <strong>7 square feet<\/strong> of the porch. Understanding how to apply geometric formulas and solve for unknown variables is key when working with shapes like cones in real-world contexts.<\/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-banner9-312.jpeg\" alt=\"\" class=\"wp-image-232546\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>. The tent instructions reveal the height at the tallest point to be 4.5 feet and the space inside to be 10.5 cubic feet. About how many square feet of the back porch will be covered by the tent? Which measure of the cone needs to be calculated to answer the problem? A. diameter B. [&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-232545","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232545","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=232545"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232545\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}