{"id":180088,"date":"2025-01-03T16:33:01","date_gmt":"2025-01-03T16:33:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=180088"},"modified":"2025-01-03T16:33:04","modified_gmt":"2025-01-03T16:33:04","slug":"1-given-the-following-equivalency-2-5-centimeters","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/03\/1-given-the-following-equivalency-2-5-centimeters\/","title":{"rendered":"1.\u00a0\u00a0\u00a0\u00a0 Given the following equivalency 2.5 centimeters\u00a0"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/files.transtutors.com\/book\/qimg\/ef9a9a59-35b6-4e6a-9d4e-6f5706967fa1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>&nbsp;inches.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Given the following equivalency 2.5 centimeters inches.<br>a) Identify the two conversion factors.<br>b) How many centimeters are there in 5.0 inches?<br>c) How many inches are there in 21.0 centimeters?<\/li>\n\n\n\n<li>A rectangle has a horizontal side measuring and a vertical side measuring 72 . Determine the perimeter. (Horizontal Side + Vertical Side)<\/li>\n\n\n\n<li>A right triangle has a base of and a height measuring . Determine the area.<\/li>\n\n\n\n<li>A box has a horizontal side measuring , a vertical side measuring , and a height of . Determine the volume.<\/li>\n\n\n\n<li>A cylinder has a radius measuring . Determine the area.<\/li>\n\n\n\n<li>A cylinder has a radius measuring and a height of . Determine the volume.<\/li>\n<\/ol>\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<p>Let&#8217;s address the problems one by one with appropriate explanations and calculations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>1. Given the following equivalency: 2.5 centimeters = 1 inch.<\/strong><\/p>\n\n\n\n<p><strong>a) Identify the two conversion factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first conversion factor is:<br>1\u00a0inch=2.5\u00a0cm1 \\text{ inch} = 2.5 \\text{ cm}.<\/li>\n\n\n\n<li>The second conversion factor is:<br>1\u00a0cm=12.5\u00a0inch=0.4\u00a0inch1 \\text{ cm} = \\frac{1}{2.5} \\text{ inch} = 0.4 \\text{ inch}.<\/li>\n<\/ul>\n\n\n\n<p><strong>b) How many centimeters are there in 5.0 inches?<\/strong><\/p>\n\n\n\n<p>To convert inches to centimeters, use the conversion factor 1&nbsp;inch=2.5&nbsp;cm1 \\text{ inch} = 2.5 \\text{ cm}: Centimeters=5.0\u2009inches\u00d72.5\u2009cm\/inch=12.5\u2009cm\\text{Centimeters} = 5.0 \\, \\text{inches} \\times 2.5 \\, \\text{cm\/inch} = 12.5 \\, \\text{cm}<\/p>\n\n\n\n<p><strong>c) How many inches are there in 21.0 centimeters?<\/strong><\/p>\n\n\n\n<p>To convert centimeters to inches, use the conversion factor 1&nbsp;cm=0.4&nbsp;inch1 \\text{ cm} = 0.4 \\text{ inch}: Inches=21.0\u2009cm\u00d70.4\u2009inch\/cm=8.4\u2009inches\\text{Inches} = 21.0 \\, \\text{cm} \\times 0.4 \\, \\text{inch\/cm} = 8.4 \\, \\text{inches}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2. A rectangle has a horizontal side measuring xx and a vertical side measuring 72. Determine the perimeter.<\/strong><\/p>\n\n\n\n<p>The perimeter of a rectangle is given by: Perimeter=2\u00d7(Length+Width)\\text{Perimeter} = 2 \\times (\\text{Length} + \\text{Width})<\/p>\n\n\n\n<p>Here, Length is xx and Width is 72. So, the perimeter is: Perimeter=2\u00d7(x+72)\\text{Perimeter} = 2 \\times (x + 72)<\/p>\n\n\n\n<p>Since xx is not given, the perimeter is expressed in terms of xx.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>3. A right triangle has a base of bb and a height of hh. Determine the area.<\/strong><\/p>\n\n\n\n<p>The area of a right triangle is given by: Area=12\u00d7Base\u00d7Height\\text{Area} = \\frac{1}{2} \\times \\text{Base} \\times \\text{Height}<\/p>\n\n\n\n<p>Substituting in the given base bb and height hh: Area=12\u00d7b\u00d7h\\text{Area} = \\frac{1}{2} \\times b \\times h<\/p>\n\n\n\n<p>Since bb and hh are not provided, the area is expressed in terms of these variables.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>4. A box has a horizontal side measuring xx, a vertical side measuring yy, and a height of zz. Determine the volume.<\/strong><\/p>\n\n\n\n<p>The volume of a box (rectangular prism) is given by: Volume=Length\u00d7Width\u00d7Height\\text{Volume} = \\text{Length} \\times \\text{Width} \\times \\text{Height}<\/p>\n\n\n\n<p>Substituting in the given dimensions: Volume=x\u00d7y\u00d7z\\text{Volume} = x \\times y \\times z<\/p>\n\n\n\n<p>Since the dimensions are represented by variables, the volume is expressed in terms of xx, yy, and zz.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>5. A cylinder has a radius of rr. Determine the area.<\/strong><\/p>\n\n\n\n<p>The surface area of a cylinder is given by the formula: Surface&nbsp;Area=2\u03c0r2+2\u03c0rh\\text{Surface Area} = 2 \\pi r^2 + 2 \\pi r h<\/p>\n\n\n\n<p>However, to calculate the area, we need to know the height hh. Without that information, the area cannot be determined.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>6. A cylinder has a radius of rr and a height of hh. Determine the volume.<\/strong><\/p>\n\n\n\n<p>The volume of a cylinder is given by the formula: Volume=\u03c0r2h\\text{Volume} = \\pi r^2 h<\/p>\n\n\n\n<p>Substituting in the given radius rr and height hh: Volume=\u03c0r2h\\text{Volume} = \\pi r^2 h<\/p>\n\n\n\n<p>This is the general formula for the volume of a cylinder. Again, without specific values for rr and hh, the answer is expressed in terms of these variables.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of Calculations:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Conversion factors: 1\u00a0inch=2.5\u00a0cm1 \\text{ inch} = 2.5 \\text{ cm} and 1\u00a0cm=0.4\u00a0inch1 \\text{ cm} = 0.4 \\text{ inch}.<\/li>\n\n\n\n<li>Perimeter of a rectangle: 2\u00d7(x+72)2 \\times (x + 72) (in terms of xx).<\/li>\n\n\n\n<li>Area of a right triangle: 12\u00d7b\u00d7h\\frac{1}{2} \\times b \\times h.<\/li>\n\n\n\n<li>Volume of a box: x\u00d7y\u00d7zx \\times y \\times z.<\/li>\n\n\n\n<li>Volume of a cylinder: \u03c0r2h\\pi r^2 h (requires height).<\/li>\n<\/ul>\n\n\n\n<p>Each of these formulas requires specific measurements to provide numerical answers, but they are presented here in their general forms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp;inches. The correct answer and explanation is: Let&#8217;s address the problems one by one with appropriate explanations and calculations. 1. Given the following equivalency: 2.5 centimeters = 1 inch. a) Identify the two conversion factors: b) How many centimeters are there in 5.0 inches? To convert inches to centimeters, use the conversion factor 1&nbsp;inch=2.5&nbsp;cm1 \\text{ [&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-180088","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180088","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=180088"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180088\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=180088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=180088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=180088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}