{"id":180165,"date":"2025-01-03T19:45:16","date_gmt":"2025-01-03T19:45:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=180165"},"modified":"2025-01-03T19:45:18","modified_gmt":"2025-01-03T19:45:18","slug":"a-stephanie-puts-30-cubes-in-a-box","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/03\/a-stephanie-puts-30-cubes-in-a-box\/","title":{"rendered":"A.\u00a0\u00a0\u00a0\u00a0 Stephanie puts 30 cubes in a box"},"content":{"rendered":"\n<p>A.&nbsp;&nbsp;&nbsp;&nbsp; Stephanie puts 30 cubes in a box. The cubes are (1)\/(2) inch on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?<\/p>\n\n\n\n<p>B.&nbsp;&nbsp;&nbsp;&nbsp; Evaluate . First find the sum as a function of ; see Exercise 2.1.4b.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A. Volume of the Box<\/h3>\n\n\n\n<p><strong>Given:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>30 cubes are placed in the box.<\/li>\n\n\n\n<li>Each cube has a side length of 12\\frac{1}{2} inch.<\/li>\n\n\n\n<li>The box holds 2 layers, with 15 cubes in each layer.<\/li>\n<\/ul>\n\n\n\n<p><strong>To find the volume of the box:<\/strong><\/p>\n\n\n\n<p>The volume of the box can be calculated by determining its dimensions: length, width, and height.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Volume of one cube:<\/strong> The formula for the volume of a cube is: Vcube=side\u00a0length3V_{\\text{cube}} = \\text{side length}^3 For one cube with a side length of 12\\frac{1}{2} inch: Vcube=(12)3=18\u2009cubic\u00a0inchesV_{\\text{cube}} = \\left(\\frac{1}{2}\\right)^3 = \\frac{1}{8} \\, \\text{cubic inches}<\/li>\n\n\n\n<li><strong>Total volume of the 30 cubes:<\/strong> Since there are 30 cubes in the box, the total volume of the cubes is: Vtotal\u00a0cubes=30\u00d718=308=3.75\u2009cubic\u00a0inchesV_{\\text{total cubes}} = 30 \\times \\frac{1}{8} = \\frac{30}{8} = 3.75 \\, \\text{cubic inches}<\/li>\n\n\n\n<li><strong>Dimensions of the box:<\/strong><ul><li>The box holds 2 layers, and each layer contains 15 cubes. Thus, the length and width of the box are based on the number of cubes in one layer.<\/li><li>Since the cubes are 12\\frac{1}{2} inch on each side, the length and width of the box are:<\/li><\/ul>length=15\u00d712=7.5\u2009inches\\text{length} = 15 \\times \\frac{1}{2} = 7.5 \\, \\text{inches} width=15\u00d712=7.5\u2009inches\\text{width} = 15 \\times \\frac{1}{2} = 7.5 \\, \\text{inches}<ul><li>The height of the box is the height of 2 layers of cubes, which is:<\/li><\/ul>height=2\u00d712=1\u2009inch\\text{height} = 2 \\times \\frac{1}{2} = 1 \\, \\text{inch}<\/li>\n\n\n\n<li><strong>Volume of the box:<\/strong> The volume of the box is calculated using the formula for the volume of a rectangular prism: Vbox=length\u00d7width\u00d7heightV_{\\text{box}} = \\text{length} \\times \\text{width} \\times \\text{height} Vbox=7.5\u00d77.5\u00d71=56.25\u2009cubic\u00a0inchesV_{\\text{box}} = 7.5 \\times 7.5 \\times 1 = 56.25 \\, \\text{cubic inches}<\/li>\n<\/ol>\n\n\n\n<p>Thus, the volume of the box is <strong>56.25 cubic 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\">B. Evaluation of the Sum<\/h3>\n\n\n\n<p>It seems like the second part of your question refers to evaluating a sum as a function of something. However, the function you&#8217;re asking to evaluate is not fully specified in the text. If the sum is in reference to a series, the sum may be something like an arithmetic or geometric series.<\/p>\n\n\n\n<p>Please clarify the sum you&#8217;re trying to evaluate, and I&#8217;ll provide a detailed explanation with the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A.&nbsp;&nbsp;&nbsp;&nbsp; Stephanie puts 30 cubes in a box. The cubes are (1)\/(2) inch on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box? B.&nbsp;&nbsp;&nbsp;&nbsp; Evaluate . First find the sum as a function of ; see Exercise 2.1.4b. The correct answer and explanation is: [&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-180165","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180165","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=180165"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180165\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=180165"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=180165"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=180165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}