{"id":227780,"date":"2025-06-06T13:28:28","date_gmt":"2025-06-06T13:28:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227780"},"modified":"2025-06-06T13:28:30","modified_gmt":"2025-06-06T13:28:30","slug":"jessica-built-a-cone-for-science-class","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/jessica-built-a-cone-for-science-class\/","title":{"rendered":"Jessica built a cone for science class."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Jessica built a cone for science class. The volume of the cone was 42 cubic inches. The radius of the cone was 2 inches. What was the approximate height of the cone? A 40 inches a. 20 inches c. 10 inches D. 4 inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><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 class=\"wp-block-paragraph\">To find the <strong>height<\/strong> of a cone, we use the formula for the <strong>volume of a cone<\/strong>: V=13\u03c0r2hV = \\frac{1}{3} \\pi r^2 h<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>VV is the volume,<\/li>\n\n\n\n<li>rr is the radius, and<\/li>\n\n\n\n<li>hh is the height.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume V=42V = 42 cubic inches<\/li>\n\n\n\n<li>Radius r=2r = 2 inches<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We need to solve for hh, the height.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Calculation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Start with the formula: 42=13\u03c0(2)2h42 = \\frac{1}{3} \\pi (2)^2 h 42=13\u03c0(4)h42 = \\frac{1}{3} \\pi (4) h 42=43\u03c0h42 = \\frac{4}{3} \\pi h<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now divide both sides by 43\u03c0\\frac{4}{3} \\pi: h=4243\u03c0h = \\frac{42}{\\frac{4}{3} \\pi} h=42\u00d734\u03c0h = \\frac{42 \\times 3}{4 \\pi} h=1264\u03c0h = \\frac{126}{4\\pi}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now approximate \u03c0\u22483.14\\pi \\approx 3.14: h\u22481264\u00d73.14h \\approx \\frac{126}{4 \\times 3.14} h\u224812612.56\u224810.03h \\approx \\frac{126}{12.56} \\approx 10.03<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the approximate height is <strong>10 inches<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C. 10 inches<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this problem, we apply the volume formula of a cone, which is one-third the product of the base area and the height. A cone\u2019s base is circular, so the area of the base is \u03c0r2\\pi r^2. When we plug this into the volume formula, it becomes V=13\u03c0r2hV = \\frac{1}{3} \\pi r^2 h.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this case, we know the volume is 42 cubic inches and the radius is 2 inches. Plugging these values into the formula lets us isolate and solve for the height hh. We square the radius (2 inches) to get 4. Multiply by \u03c0\\pi and then by 13\\frac{1}{3}, giving 43\u03c0\\frac{4}{3} \\pi. We set this equal to the known volume (42) and solve algebraically to isolate hh.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After rearranging, we divide 42 by 43\u03c0\\frac{4}{3} \\pi, which simplifies to 1264\u03c0\\frac{126}{4 \\pi}. Using the approximation \u03c0\u22483.14\\pi \\approx 3.14, we compute 4\u00d73.14=12.564 \\times 3.14 = 12.56, then divide 126 by 12.56. This results in approximately 10.03 inches.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The closest whole number is 10, so the best approximation of the cone\u2019s height is 10 inches. This matches option <strong>C<\/strong>, making it the correct answer. This process shows how mathematical formulas, substitutions, and approximations work together to solve real-world geometry problems.<\/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-banner9-139.jpeg\" alt=\"\" class=\"wp-image-227781\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Jessica built a cone for science class. The volume of the cone was 42 cubic inches. The radius of the cone was 2 inches. What was the approximate height of the cone? A 40 inches a. 20 inches c. 10 inches D. 4 inches The Correct Answer and Explanation is: To find the height of [&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-227780","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227780","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=227780"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227780\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}