{"id":22014,"date":"2025-06-16T08:48:55","date_gmt":"2025-06-16T08:48:55","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22014"},"modified":"2025-06-16T08:48:59","modified_gmt":"2025-06-16T08:48:59","slug":"the-circumference-of-a-circle-is-28-pi-meters","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-circumference-of-a-circle-is-28-pi-meters\/","title":{"rendered":"The circumference of a circle is 28 pi meters"},"content":{"rendered":"\n<p>The circumference of a circle is 28 pi meters. What is its area in terms of pi?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Answer:<\/strong> The area of the circle is <strong>49\u03c0 square meters<\/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>The problem gives the circumference of a circle as 28\u03c028\\pi meters and asks for the area in terms of \u03c0\\pi.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 1: Recall the formulas for a circle<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Circumference C=2\u03c0rC = 2\\pi r<\/li>\n\n\n\n<li>Area A=\u03c0r2A = \\pi r^2<\/li>\n<\/ul>\n\n\n\n<p>where rr is the radius of the circle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 2: Use the circumference to find the radius<\/strong><\/p>\n\n\n\n<p>Given C=28\u03c0C = 28\\pi, 28\u03c0=2\u03c0r28\\pi = 2\\pi r<\/p>\n\n\n\n<p>Divide both sides by 2\u03c02\\pi: r=28\u03c02\u03c0=282=14r = \\frac{28\\pi}{2\\pi} = \\frac{28}{2} = 14<\/p>\n\n\n\n<p>So, the radius of the circle is 14 meters.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 3: Calculate the area using the radius<\/strong><\/p>\n\n\n\n<p>Using the area formula, A=\u03c0r2=\u03c0(14)2=\u03c0\u00d7196=196\u03c0A = \\pi r^2 = \\pi (14)^2 = \\pi \\times 196 = 196\\pi<\/p>\n\n\n\n<p>Wait \u2014 the answer above states 49\u03c0, so let&#8217;s double-check the calculation:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Double-checking:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Circumference = 28\u03c028\\pi<\/li>\n\n\n\n<li>From C=2\u03c0rC = 2\\pi r, r=C2\u03c0=28\u03c02\u03c0=14r = \\frac{C}{2\\pi} = \\frac{28\\pi}{2\\pi} = 14<\/li>\n\n\n\n<li>Area = \u03c0r2=\u03c0\u00d7142=\u03c0\u00d7196=196\u03c0\\pi r^2 = \\pi \\times 14^2 = \\pi \\times 196 = 196\\pi<\/li>\n<\/ul>\n\n\n\n<p>So the area is actually <strong>196\u03c0 square meters<\/strong>, not 49\u03c0.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Final corrected answer:<\/strong> The area is <strong>196\u03c0 square meters<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start with circumference formula to find radius.<\/li>\n\n\n\n<li>Substitute radius into area formula.<\/li>\n\n\n\n<li>Carefully perform arithmetic.<\/li>\n\n\n\n<li>The radius is 14 meters.<\/li>\n\n\n\n<li>The area is \u03c0\u00d7142=196\u03c0\\pi \\times 14^2 = 196\\pi.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the area of the circle in terms of \u03c0\\pi is <strong>196\u03c0 square meters<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The circumference of a circle is 28 pi meters. What is its area in terms of pi? The correct answer and explanation is: Answer: The area of the circle is 49\u03c0 square meters. Explanation: The problem gives the circumference of a circle as 28\u03c028\\pi meters and asks for the area in terms of \u03c0\\pi. Step [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-22014","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22014","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=22014"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22014\/revisions"}],"predecessor-version":[{"id":22015,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22014\/revisions\/22015"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}