{"id":205887,"date":"2025-03-25T18:58:26","date_gmt":"2025-03-25T18:58:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205887"},"modified":"2025-03-25T18:58:28","modified_gmt":"2025-03-25T18:58:28","slug":"find-the-volume-of-a-regular-hexagonal-pyramid-if-the-perpendicular-height-is-16-0cm-and-the-side-of-the-base-is-3-0cm","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/find-the-volume-of-a-regular-hexagonal-pyramid-if-the-perpendicular-height-is-16-0cm-and-the-side-of-the-base-is-3-0cm\/","title":{"rendered":"Find the volume of a regular hexagonal pyramid if the perpendicular height is 16.0cm and the side of the base is 3.0cm"},"content":{"rendered":"\n<p>Find the volume of a regular hexagonal pyramid if the perpendicular height is 16.0cm and the side of the base is 3.0cm.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the volume of a regular hexagonal pyramid, we use the formula:<\/p>\n\n\n\n<p>[<br>V = \\frac{1}{3} \\times B \\times h<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( B ) is the area of the hexagonal base<\/li>\n\n\n\n<li>( h ) is the perpendicular height of the pyramid<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Find the Area of the Hexagonal Base<\/strong><\/h3>\n\n\n\n<p>A regular hexagon can be divided into <strong>six<\/strong> equilateral triangles. The area of one equilateral triangle with side length ( s ) is:<\/p>\n\n\n\n<p>[<br>A_{\\triangle} = \\frac{\\sqrt{3}}{4} s^2<br>]<\/p>\n\n\n\n<p>Since the hexagon consists of 6 such triangles, its total area is:<\/p>\n\n\n\n<p>[<br>B = 6 \\times \\frac{\\sqrt{3}}{4} s^2<br>]<\/p>\n\n\n\n<p>Substituting ( s = 3.0 ) cm:<\/p>\n\n\n\n<p>[<br>B = 6 \\times \\frac{\\sqrt{3}}{4} \\times (3.0)^2<br>]<\/p>\n\n\n\n<p>[<br>B = 6 \\times \\frac{\\sqrt{3}}{4} \\times 9<br>]<\/p>\n\n\n\n<p>[<br>B = 6 \\times \\frac{9\\sqrt{3}}{4}<br>]<\/p>\n\n\n\n<p>[<br>B = \\frac{54\\sqrt{3}}{4}<br>]<\/p>\n\n\n\n<p>[<br>B = \\frac{27\\sqrt{3}}{2} \\approx 23.38 \\text{ cm}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Find the Volume<\/strong><\/h3>\n\n\n\n<p>Now, using ( h = 16.0 ) cm:<\/p>\n\n\n\n<p>[<br>V = \\frac{1}{3} \\times 23.38 \\times 16.0<br>]<\/p>\n\n\n\n<p>[<br>V = \\frac{374.08}{3}<br>]<\/p>\n\n\n\n<p>[<br>V \\approx 124.69 \\text{ cm}^3<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p>[<br>\\mathbf{124.69 \\text{ cm}^3}<br>]<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-1447.png\" alt=\"\" class=\"wp-image-205891\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the volume of a regular hexagonal pyramid if the perpendicular height is 16.0cm and the side of the base is 3.0cm. The correct answer and explanation is : To find the volume of a regular hexagonal pyramid, we use the formula: [V = \\frac{1}{3} \\times B \\times h] where: Step 1: Find the Area [&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-205887","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205887","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=205887"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205887\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}