{"id":236223,"date":"2025-06-16T06:18:57","date_gmt":"2025-06-16T06:18:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236223"},"modified":"2025-06-16T06:18:59","modified_gmt":"2025-06-16T06:18:59","slug":"for-a-circle-that-has-a-diameter-of-54-inches-what-is-the-circumference-in-feet-and-inches","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/for-a-circle-that-has-a-diameter-of-54-inches-what-is-the-circumference-in-feet-and-inches\/","title":{"rendered":"For a circle that has a diameter of 54 inches, what is the circumference in feet and inches"},"content":{"rendered":"\n<p>For a circle that has a diameter of 54 inches, what is the circumference in feet and inches? Give your answer to the nearest 1\/8 inch: (12 inches = 1 foot) 102-2.6-8: Find the radius of a circle that has a circumference of 841 cm. 102-2.6-9: Find the area of a circle, in terms of \u00cf\u20ac, that has a radius of 6 inches.<\/p>\n\n\n\n<p><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><strong>102-2.6-7: Circumference of a Circle with Diameter 54 Inches<\/strong><\/p>\n\n\n\n<p>The formula for the circumference CCC of a circle is:C=\u03c0\u00d7dC = \\pi \\times dC=\u03c0\u00d7d<\/p>\n\n\n\n<p>Given diameter d=54d = 54d=54 inches:C=\u03c0\u00d754\u22483.1416\u00d754=169.6464&nbsp;inchesC = \\pi \\times 54 \\approx 3.1416 \\times 54 = 169.6464 \\text{ inches}C=\u03c0\u00d754\u22483.1416\u00d754=169.6464&nbsp;inches<\/p>\n\n\n\n<p>Now convert this to feet and inches:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>There are 12 inches in a foot.<\/li>\n\n\n\n<li>Divide 169.6464169.6464169.6464 by 12:<\/li>\n<\/ul>\n\n\n\n<p>169.6464\u00f712=14&nbsp;feet&nbsp;and&nbsp;1.6464&nbsp;inches169.6464 \\div 12 = 14 \\text{ feet and } 1.6464 \\text{ inches}169.6464\u00f712=14&nbsp;feet&nbsp;and&nbsp;1.6464&nbsp;inches<\/p>\n\n\n\n<p>To convert the decimal inches to the nearest 1\/8 inch:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply 0.6464 by 8:<\/li>\n<\/ul>\n\n\n\n<p>0.6464\u00d78=5.17120.6464 \\times 8 = 5.17120.6464\u00d78=5.1712<\/p>\n\n\n\n<p>Rounded to the nearest whole number: <strong>5<\/strong><\/p>\n\n\n\n<p>So, the remaining fraction is 58\\frac{5}{8}85\u200b inch.<\/p>\n\n\n\n<p><strong>Answer:<\/strong> 14&nbsp;feet&nbsp;158&nbsp;inches\\boxed{14 \\text{ feet } 1 \\frac{5}{8} \\text{ inches}}14&nbsp;feet&nbsp;185\u200b&nbsp;inches\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>102-2.6-8: Radius from Circumference 841 cm<\/strong><\/p>\n\n\n\n<p>Use the circumference formula:C=2\u03c0rC = 2\\pi rC=2\u03c0r<\/p>\n\n\n\n<p>Given C=841C = 841C=841 cm:r=C2\u03c0=8412\u00d73.1416\u22488416.2832\u2248133.84&nbsp;cmr = \\frac{C}{2\\pi} = \\frac{841}{2 \\times 3.1416} \\approx \\frac{841}{6.2832} \\approx 133.84 \\text{ cm}r=2\u03c0C\u200b=2\u00d73.1416841\u200b\u22486.2832841\u200b\u2248133.84&nbsp;cm<\/p>\n\n\n\n<p><strong>Answer:<\/strong> 133.84&nbsp;cm\\boxed{133.84 \\text{ cm}}133.84&nbsp;cm\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>102-2.6-9: Area of Circle in Terms of \u03c0\\pi\u03c0, Radius 6 Inches<\/strong><\/p>\n\n\n\n<p>The area AAA of a circle is:A=\u03c0r2A = \\pi r^2A=\u03c0r2<\/p>\n\n\n\n<p>Given radius r=6r = 6r=6 inches:A=\u03c0\u00d762=\u03c0\u00d736A = \\pi \\times 6^2 = \\pi \\times 36A=\u03c0\u00d762=\u03c0\u00d736<\/p>\n\n\n\n<p><strong>Answer:<\/strong> 36\u03c0&nbsp;in2\\boxed{36\\pi \\text{ in}^2}36\u03c0&nbsp;in2\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>The circumference of a circle depends directly on its diameter. The relationship is expressed through the formula C=\u03c0dC = \\pi dC=\u03c0d, where \u03c0\\pi\u03c0 represents the mathematical constant approximately equal to 3.1416. When a diameter of 54 inches is used, multiplying by \u03c0\\pi\u03c0 gives an approximate circumference of 169.6464 inches. Converting to feet involves dividing the total inches by 12, yielding 14 full feet and a remainder of approximately 1.6464 inches. This remaining portion is converted to eighths by multiplying the decimal by 8 and rounding to the nearest whole number. This gives a final answer in mixed units\u2014feet and inches\u2014precise to the nearest eighth inch.<\/p>\n\n\n\n<p>When reversing the process\u2014finding the radius from a given circumference\u2014the circumference formula is rearranged to isolate the radius: r=C2\u03c0r = \\frac{C}{2\\pi}r=2\u03c0C\u200b. Substituting 841 cm for the circumference and dividing by 2\u03c02\\pi2\u03c0 gives a radius of approximately 133.84 cm. This shows how circumference and radius scale proportionally in circular geometry.<\/p>\n\n\n\n<p>To find the area of a circle in terms of \u03c0\\pi\u03c0, the expression A=\u03c0r2A = \\pi r^2A=\u03c0r2 is used. For a radius of 6 inches, squaring the radius gives 36, which is then multiplied by \u03c0\\pi\u03c0. The area remains in terms of \u03c0\\pi\u03c0 for exactness, avoiding any rounding errors associated with decimal approximations. This approach is particularly useful in algebraic or symbolic expressions.<\/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-banner10-146.jpeg\" alt=\"\" class=\"wp-image-236224\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>For a circle that has a diameter of 54 inches, what is the circumference in feet and inches? Give your answer to the nearest 1\/8 inch: (12 inches = 1 foot) 102-2.6-8: Find the radius of a circle that has a circumference of 841 cm. 102-2.6-9: Find the area of a circle, in terms of [&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-236223","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236223","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=236223"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236223\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}