{"id":226883,"date":"2025-06-05T16:34:37","date_gmt":"2025-06-05T16:34:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226883"},"modified":"2025-06-05T16:34:39","modified_gmt":"2025-06-05T16:34:39","slug":"o-find-the-diameter-of-the-larger-circle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/o-find-the-diameter-of-the-larger-circle\/","title":{"rendered":"O find the diameter of the larger circle"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">o find the diameter of the larger circle<br>the circumference of the circle is 56.52 and the circumference of the smaller circle is 28.26 use a proportion to find the diameter of the larger circle<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the diameter of the larger circle using a proportion, we start with the relationship between <strong>circumference<\/strong> and <strong>diameter<\/strong>: Circumference=\u03c0\u00d7Diameter\\text{Circumference} = \\pi \\times \\text{Diameter}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Circumference of the <strong>larger circle<\/strong>: 56.52 units<\/li>\n\n\n\n<li>Circumference of the <strong>smaller circle<\/strong>: 28.26 units<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s assume:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Diameter of the smaller circle = <em>d\u2081<\/em><\/li>\n\n\n\n<li>Diameter of the larger circle = <em>d\u2082<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">From the formula above: Circumference&nbsp;of&nbsp;larger&nbsp;circleCircumference&nbsp;of&nbsp;smaller&nbsp;circle=d2d1\\frac{\\text{Circumference of larger circle}}{\\text{Circumference of smaller circle}} = \\frac{d_2}{d_1}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the given values: 56.5228.26=d2d1\\frac{56.52}{28.26} = \\frac{d_2}{d_1}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now simplify: 2=d2d12 = \\frac{d_2}{d_1}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This tells us that the diameter of the larger circle is <strong>twice<\/strong> that of the smaller circle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the actual diameter of the larger circle, we first compute the diameter of the smaller circle using: Circumference=\u03c0\u00d7Diameter\u21d2Diameter=Circumference\u03c0\\text{Circumference} = \\pi \\times \\text{Diameter} \\Rightarrow \\text{Diameter} = \\frac{\\text{Circumference}}{\\pi}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, d1=28.26\u03c0\u224828.263.1416\u22489d_1 = \\frac{28.26}{\\pi} \\approx \\frac{28.26}{3.1416} \\approx 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, d2=2\u00d7d1=2\u00d79=18d_2 = 2 \\times d_1 = 2 \\times 9 = 18<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The diameter of the larger circle is 18 units.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem is based on understanding proportional relationships between the dimensions of circles. The key geometric formula at play is the relationship between a circle\u2019s circumference (C) and its diameter (d), given by the formula: C=\u03c0\u00d7dC = \\pi \\times d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since both circles are true circles, their circumferences and diameters will maintain a consistent ratio. This means that the ratio of their circumferences is equal to the ratio of their diameters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We\u2019re told the larger circle has a circumference of 56.52 units and the smaller one 28.26 units. By dividing these, we get: 56.5228.26=2\\frac{56.52}{28.26} = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This tells us the larger circle&#8217;s diameter is twice the smaller\u2019s. To determine the actual size, we calculate the smaller circle\u2019s diameter by dividing its circumference by \u03c0 (approximately 3.1416), which gives us: 28.263.1416\u22489&nbsp;units\\frac{28.26}{3.1416} \\approx 9 \\text{ units}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplying by 2 gives us the larger circle&#8217;s diameter: 9\u00d72=18&nbsp;units9 \\times 2 = 18 \\text{ units}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This approach shows how proportional reasoning, along with understanding formulas involving \u03c0, allows us to find unknown dimensions. It\u2019s a practical application of algebra and geometry working together.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-249.jpeg\" alt=\"\" class=\"wp-image-226884\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>o find the diameter of the larger circlethe circumference of the circle is 56.52 and the circumference of the smaller circle is 28.26 use a proportion to find the diameter of the larger circle The Correct Answer and Explanation is: To find the diameter of the larger circle using a proportion, we start with the [&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-226883","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226883","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=226883"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226883\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}