Ben and Lund were asked to find the area of a circle with a diameter of 9 cm.
Use their work to answer questionis 1-2.
AREA OF A CIRCLE
BEN
A-3.14 (92)
A-3.14 (81)
A-254.34 cm\u00b2
1 Describe Ben’s mistake in solving for the area of the circle.
LUNA
A-3.14 (45\u00b2)
A-3.14 (9)
A-28.26 cm\u00b2<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s break down Ben’s and Luna’s mistakes in solving for the area of the circle and identify the correct calculation.<\/p>\n\n\n\n Ben uses the formula for the area of a circle:<\/p>\n\n\n\n [ where (r) is the radius of the circle, and (\\pi \\approx 3.14).<\/p>\n\n\n\n Ben was given the diameter<\/strong> of the circle, which is 9 cm. The radius<\/strong> is half the diameter, so:<\/p>\n\n\n\n [ However, in Ben’s work, he incorrectly used 9 as the radius, which is the diameter of the circle. He should have used 4.5 as the radius. His equation was:<\/p>\n\n\n\n [ This is incorrect because Ben used the diameter instead of the radius in his calculation.<\/p>\n\n\n\n Luna also uses the correct formula for the area of a circle:<\/p>\n\n\n\n [ She correctly recognizes that the diameter is 9 cm, so the radius should be 4.5 cm. However, in Luna\u2019s work, she mistakenly calculates the radius as 9 cm again (instead of 4.5 cm), which leads to an error in her calculation. Luna writes:<\/p>\n\n\n\n [ While this answer is correct, the error in Luna’s steps is the value she incorrectly wrote for the radius \u2014 it should be 4.5 cm<\/strong>, but Luna wrote 9 cm<\/strong>. Once she correctly recognizes the radius, the calculation of the area becomes accurate.<\/p>\n\n\n\n Now that we’ve identified Ben and Luna\u2019s mistakes, let’s correctly calculate the area of the circle. The radius of the circle is:<\/p>\n\n\n\n [ The formula for the area of the circle is:<\/p>\n\n\n\n [ The correct area of the circle, rounded to the nearest hundredth, is:<\/p>\n\n\n\n [ The key here is recognizing the difference between the diameter<\/strong> and the radius<\/strong>. The diameter of the circle is given as 9 cm, but the formula for the area of a circle requires the radius, which is half of the diameter. Ben mistakenly used the diameter as the radius, leading to an inflated area, while Luna mistakenly calculated using the radius, but the value she used for the radius was incorrectly written down. The correct radius, (r = 4.5 \\, \\text{cm}), should be substituted into the formula for the area of a circle:<\/p>\n\n\n\n [ This is the correct solution.<\/p>\n","protected":false},"excerpt":{"rendered":" Ben and Lund were asked to find the area of a circle with a diameter of 9 cm.Use their work to answer questionis 1-2.AREA OF A CIRCLEBENA-3.14 (92)A-3.14 (81)A-254.34 cm\u00b21 Describe Ben’s mistake in solving for the area of the circle.LUNAA-3.14 (45\u00b2)A-3.14 (9)A-28.26 cm\u00b2 The Correct Answer and Explanation is: Let’s break down Ben’s and […]<\/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-165176","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165176","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=165176"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165176\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Ben’s Mistake:<\/h3>\n\n\n\n
A = \\pi r^2
]<\/p>\n\n\n\n
r = \\frac{9}{2} = 4.5 \\text{ cm}
]<\/p>\n\n\n\n
A = 3.14 \\times (9^2) = 3.14 \\times 81 = 254.34 \\, \\text{cm}^2
]<\/p>\n\n\n\nLuna’s Mistake:<\/h3>\n\n\n\n
A = \\pi r^2
]<\/p>\n\n\n\n
A = 3.14 \\times (4.5^2) = 3.14 \\times 20.25 = 28.26 \\, \\text{cm}^2
]<\/p>\n\n\n\nCorrect Calculation:<\/h3>\n\n\n\n
r = \\frac{9}{2} = 4.5 \\, \\text{cm}
]<\/p>\n\n\n\n
A = \\pi r^2 = 3.14 \\times (4.5^2) = 3.14 \\times 20.25 = 63.585 \\, \\text{cm}^2
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
A \\approx 63.59 \\, \\text{cm}^2
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n
A = \\pi r^2 = 3.14 \\times (4.5)^2 = 63.59 \\, \\text{cm}^2
]<\/p>\n\n\n\n