{"id":245548,"date":"2025-07-06T08:51:35","date_gmt":"2025-07-06T08:51:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245548"},"modified":"2025-07-06T08:51:37","modified_gmt":"2025-07-06T08:51:37","slug":"calculate-the-volumes-in-of-5-metre-lengths-of-the-beams","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/calculate-the-volumes-in-of-5-metre-lengths-of-the-beams\/","title":{"rendered":"Calculate the volumes, in, of 5-metre lengths of the beams."},"content":{"rendered":"\n<p>The diagrams in Fig. 15.9 show the cross-sections of steel beams. All dimensions are in cm. Calculate the volumes, in<br>, of 5-metre lengths of the beams.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-221.png\" alt=\"\" class=\"wp-image-245549\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here are the calculated volumes for the 5-metre lengths of each steel beam.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Volume of beam a = 5000 cm\u00b3<\/strong><\/li>\n\n\n\n<li><strong>Volume of beam b = 5500 cm\u00b3<\/strong><\/li>\n\n\n\n<li><strong>Volume of beam c = 7500 cm\u00b3<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>To find the volume of each steel beam, we use the formula:<br>Volume = Cross-sectional Area \u00d7 Length<\/p>\n\n\n\n<p>The problem provides the cross-section dimensions in centimeters (cm) and the length of the beams in meters. To calculate the volume in cubic centimeters (cm\u00b3), we must first convert the length to centimeters.<\/p>\n\n\n\n<p>Length = 5 meters = 5 \u00d7 100 = 500 cm.<\/p>\n\n\n\n<p>Next, we calculate the cross-sectional area for each of the three beams.<\/p>\n\n\n\n<p><strong>Beam a (L-shape):<\/strong><br>We can split this shape into two rectangles to find its area.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A vertical rectangle with dimensions 1 cm wide by (5 cm + 1 cm) = 6 cm tall. Its area is 1 \u00d7 6 = 6 cm\u00b2.<\/li>\n\n\n\n<li>A horizontal rectangle with dimensions 4 cm long by 1 cm tall. Its area is 4 \u00d7 1 = 4 cm\u00b2.<br>The total cross-sectional area is 6 cm\u00b2 + 4 cm\u00b2 = 10 cm\u00b2.<br><strong>Volume a<\/strong>\u00a0= 10 cm\u00b2 \u00d7 500 cm =\u00a0<strong>5000 cm\u00b3<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p><strong>Beam b (T-shape):<\/strong><br>This shape can also be split into two rectangles.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The top horizontal rectangle is 6 cm wide by 1 cm tall. Its area is 6 \u00d7 1 = 6 cm\u00b2.<\/li>\n\n\n\n<li>The vertical stem is 5 cm tall by 1 cm wide. Its area is 5 \u00d7 1 = 5 cm\u00b2.<br>The total cross-sectional area is 6 cm\u00b2 + 5 cm\u00b2 = 11 cm\u00b2.<br><strong>Volume b<\/strong>\u00a0= 11 cm\u00b2 \u00d7 500 cm =\u00a0<strong>5500 cm\u00b3<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p><strong>Beam c (U-shape):<\/strong><br>The area can be calculated by viewing it as a large outer rectangle with a smaller inner rectangle removed.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The area of the outer rectangle is 6 cm \u00d7 4.5 cm = 27 cm\u00b2.<\/li>\n\n\n\n<li>The area of the inner, empty rectangle is 4 cm \u00d7 3 cm = 12 cm\u00b2.<br>The cross-sectional area is the difference: 27 cm\u00b2 \u2013 12 cm\u00b2 = 15 cm\u00b2.<br><strong>Volume c<\/strong>\u00a0= 15 cm\u00b2 \u00d7 500 cm =\u00a0<strong>7500 cm\u00b3<\/strong>.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-657.jpeg\" alt=\"\" class=\"wp-image-245550\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The diagrams in Fig. 15.9 show the cross-sections of steel beams. All dimensions are in cm. Calculate the volumes, in, of 5-metre lengths of the beams. The Correct Answer and Explanation is: Here are the calculated volumes for the 5-metre lengths of each steel beam. Explanation To find the volume of each steel beam, we [&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-245548","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245548","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=245548"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245548\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245548"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245548"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245548"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}