{"id":205432,"date":"2025-03-24T16:09:36","date_gmt":"2025-03-24T16:09:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205432"},"modified":"2025-03-24T16:09:41","modified_gmt":"2025-03-24T16:09:41","slug":"a-sandbox-in-the-shape-of-a-rectangular-prism-has-a-length-of-47","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/24\/a-sandbox-in-the-shape-of-a-rectangular-prism-has-a-length-of-47\/","title":{"rendered":"A sandbox in the shape of a rectangular prism has a length of 47"},"content":{"rendered":"\n

A sandbox in the shape of a rectangular prism has a length of 47 ?inches and a width of 30 ?inches. Jack uses bags of sand to fill the sandbox to a depth of 9 ?inches. Each bag of sand has a volume of 0.5 ?cubic foot. What is the minimum number of bags of sand that must be purchased to fill the sandbox?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Answer:<\/h3>\n\n\n\n

Jack needs a minimum of 8 bags<\/strong> of sand to fill the sandbox.<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine the number of bags of sand needed, we follow these steps:<\/p>\n\n\n\n

Step 1: Calculate the Volume of the Sandbox<\/strong><\/h4>\n\n\n\n

The sandbox is a rectangular prism, so we use the volume formula: V=length\u00d7width\u00d7heightV = \\text{length} \\times \\text{width} \\times \\text{height}<\/p>\n\n\n\n

Given:<\/p>\n\n\n\n

    \n
  • Length = 47 inches<\/strong><\/li>\n\n\n\n
  • Width = 30 inches<\/strong><\/li>\n\n\n\n
  • Depth (Height) = 9 inches<\/strong><\/li>\n<\/ul>\n\n\n\n

    V=47\u00d730\u00d79V = 47 \\times 30 \\times 9 V=12,690 cubic inchesV = 12,690 \\text{ cubic inches}<\/p>\n\n\n\n

    Step 2: Convert Cubic Inches to Cubic Feet<\/strong><\/h4>\n\n\n\n

    Since 1 cubic foot = 1,728 cubic inches<\/strong>, we convert: 12,6901,728\u22487.35 cubic feet\\frac{12,690}{1,728} \\approx 7.35 \\text{ cubic feet}<\/p>\n\n\n\n

    Step 3: Determine the Number of Bags<\/strong><\/h4>\n\n\n\n

    Each bag contains 0.5 cubic feet<\/strong> of sand. The number of bags needed is: 7.350.5=14.7\\frac{7.35}{0.5} = 14.7<\/p>\n\n\n\n

    Since we cannot buy a fraction of a bag, we round up to 15 bags<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Why Rounding Up Matters<\/strong><\/h3>\n\n\n\n

    Even though 14.7 suggests we need “almost” 15 bags, if we only buy 14, we will not have enough sand to completely fill the sandbox. Always round up in cases where fractional values occur.<\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/strong><\/h3>\n\n\n\n

    Jack needs to purchase 15 bags<\/strong> of sand.<\/p>\n\n\n\n

    \n\n\n\n

    Generated Image:<\/strong><\/h3>\n\n\n\n

    An illustration showing a rectangular sandbox filled with sand, labeled with its dimensions. A few bags of sand are placed next to it, labeled “0.5 cubic feet each.” The depth of the sand inside is shown clearly.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A sandbox in the shape of a rectangular prism has a length of 47 ?inches and a width of 30 ?inches. Jack uses bags of sand to fill the sandbox to a depth of 9 ?inches. Each bag of sand has a volume of 0.5 ?cubic foot. What is the minimum number of bags of […]<\/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-205432","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205432","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=205432"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205432\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}