{"id":93223,"date":"2025-06-01T11:45:19","date_gmt":"2025-06-01T11:45:19","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93223"},"modified":"2025-06-01T11:45:19","modified_gmt":"2025-06-01T11:45:19","slug":"a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/","title":{"rendered":"A wire is in the shape of a circle. It is straightened and reshaped in"},"content":{"rendered":"

A wire is in the shape of a circle. It is straightened and reshaped into a rectangle whose sides are in the ratio 6 : 7. If the area of the rectangle is 4200 sq. cm, the radius of circle is, approximately :<\/p>\n

[amp_mcq option1=”40 cm” option2=”42 cm” option3=”41 cm” option4=”35 cm” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle’s area and side ratio.
\n<\/section>\n
\n– The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle.
\n– Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x.
\n– Area of rectangle = length * width = (6x)(7x) = 42x\u00b2.
\n– Given area = 4200 sq. cm.
\n– 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm.
\n– Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm.
\n– Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm.
\n– Circumference of the circle = 2\u03c0r, where r is the radius.
\n– Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm.
\n– \u03c0r = 130 cm.
\n– r = 130 \/ \u03c0.
\n– Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm.
\n– Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm.
\n– The value approximately matches 41 cm.
\n<\/section>\n
\nThis problem connects the concepts of area and perimeter for different geometric shapes. The key insight is that when a wire is reshaped, its total length (which corresponds to the perimeter of the original shape and the new shape) remains constant.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A wire is in the shape of a circle. It is straightened and reshaped into a rectangle whose sides are in the ratio 6 : 7. If the area of the rectangle is 4200 sq. cm, the radius of circle is, approximately : [amp_mcq option1=”40 cm” option2=”42 cm” option3=”41 cm” option4=”35 cm” correct=”option3″] This question … <\/p>\n

Detailed SolutionA wire is in the shape of a circle. It is straightened and reshaped in<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1105,1102],"class_list":["post-93223","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA wire is in the shape of a circle. It is straightened and reshaped in<\/title>\n<meta name=\"description\" content=\"The correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle's area and side ratio. - The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle. - Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x. - Area of rectangle = length * width = (6x)(7x) = 42x\u00b2. - Given area = 4200 sq. cm. - 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm. - Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm. - Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm. - Circumference of the circle = 2\u03c0r, where r is the radius. - Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm. - \u03c0r = 130 cm. - r = 130 \/ \u03c0. - Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm. - Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm. - The value approximately matches 41 cm.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A wire is in the shape of a circle. It is straightened and reshaped in\" \/>\n<meta property=\"og:description\" content=\"The correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle's area and side ratio. - The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle. - Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x. - Area of rectangle = length * width = (6x)(7x) = 42x\u00b2. - Given area = 4200 sq. cm. - 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm. - Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm. - Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm. - Circumference of the circle = 2\u03c0r, where r is the radius. - Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm. - \u03c0r = 130 cm. - r = 130 \/ \u03c0. - Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm. - Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm. - The value approximately matches 41 cm.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:45:19+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A wire is in the shape of a circle. It is straightened and reshaped in","description":"The correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle's area and side ratio. - The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle. - Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x. - Area of rectangle = length * width = (6x)(7x) = 42x\u00b2. - Given area = 4200 sq. cm. - 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm. - Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm. - Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm. - Circumference of the circle = 2\u03c0r, where r is the radius. - Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm. - \u03c0r = 130 cm. - r = 130 \/ \u03c0. - Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm. - Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm. - The value approximately matches 41 cm.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/","og_locale":"en_US","og_type":"article","og_title":"A wire is in the shape of a circle. It is straightened and reshaped in","og_description":"The correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle's area and side ratio. - The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle. - Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x. - Area of rectangle = length * width = (6x)(7x) = 42x\u00b2. - Given area = 4200 sq. cm. - 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm. - Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm. - Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm. - Circumference of the circle = 2\u03c0r, where r is the radius. - Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm. - \u03c0r = 130 cm. - r = 130 \/ \u03c0. - Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm. - Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm. - The value approximately matches 41 cm.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:45:19+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/","name":"A wire is in the shape of a circle. It is straightened and reshaped in","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:45:19+00:00","dateModified":"2025-06-01T11:45:19+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is approximately 41 cm. The radius of the circle is determined by equating its circumference to the perimeter of the rectangle, which is derived from the rectangle's area and side ratio. - The wire is reshaped, meaning the perimeter of the circle is equal to the perimeter of the rectangle. - Rectangle sides are in the ratio 6:7. Let the sides be 6x and 7x. - Area of rectangle = length * width = (6x)(7x) = 42x\u00b2. - Given area = 4200 sq. cm. - 42x\u00b2 = 4200 => x\u00b2 = 4200 \/ 42 = 100 => x = 10 cm. - Sides of the rectangle are 6 * 10 = 60 cm and 7 * 10 = 70 cm. - Perimeter of rectangle = 2 * (length + width) = 2 * (60 + 70) = 2 * 130 = 260 cm. - Circumference of the circle = 2\u03c0r, where r is the radius. - Perimeter of circle = Perimeter of rectangle => 2\u03c0r = 260 cm. - \u03c0r = 130 cm. - r = 130 \/ \u03c0. - Using the approximation \u03c0 \u2248 3.14: r \u2248 130 \/ 3.14 \u2248 41.40 cm. - Using the approximation \u03c0 \u2248 22\/7: r \u2248 130 \/ (22\/7) = 130 * 7 \/ 22 = 910 \/ 22 = 455 \/ 11 \u2248 41.36 cm. - The value approximately matches 41 cm.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-wire-is-in-the-shape-of-a-circle-it-is-straightened-and-reshaped-in\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"A wire is in the shape of a circle. 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