{"id":92932,"date":"2025-06-01T11:37:02","date_gmt":"2025-06-01T11:37:02","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92932"},"modified":"2025-06-01T11:37:02","modified_gmt":"2025-06-01T11:37:02","slug":"consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/","title":{"rendered":"Consider a square of side length 2 m. What is the difference of the ar"},"content":{"rendered":"

Consider a square of side length 2 m. What is the difference of the areas of the circumscribed circle and the inscribed circle (in m\u00b2) ?<\/p>\n

[amp_mcq option1=”3\u03c0\/2″ option2=”\u03c0\/2″ option3=”2\u03c0” option4=”\u03c0” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is \u03c0.
\n<\/section>\n
\nLet the side length of the square be s = 2 m.
\nThe inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square.
\nRadius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m.
\nArea of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2.<\/p>\n

The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square.
\nDiagonal of the square = s * \u221a2 = 2 * \u221a2 m.
\nRadius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m.
\nArea of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2.<\/p>\n

The difference of the areas = Area of circumscribed circle – Area of inscribed circle
\nDifference = 2\u03c0 m\u00b2 – \u03c0 m\u00b2 = \u03c0 m\u00b2.
\n<\/section>\n

\nFor a square of side ‘s’, the radius of the inscribed circle is s\/2, and the radius of the circumscribed circle is (s\u221a2)\/2 = s\/\u221a2. The ratio of the radii is (s\/\u221a2) \/ (s\/2) = \u221a2, and the ratio of the areas is (Area_circum \/ Area_in) = (\u03c0 * (s\/\u221a2)\u00b2) \/ (\u03c0 * (s\/2)\u00b2) = (s\u00b2\/2) \/ (s\u00b2\/4) = 2. The area of the circumscribed circle is always twice the area of the inscribed circle for any square.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Consider a square of side length 2 m. What is the difference of the areas of the circumscribed circle and the inscribed circle (in m\u00b2) ? [amp_mcq option1=”3\u03c0\/2″ option2=”\u03c0\/2″ option3=”2\u03c0” option4=”\u03c0” correct=”option4″] This question was previously asked in UPSC CISF-AC-EXE – 2021 Download PDFAttempt Online The correct answer is \u03c0. Let the side length of … <\/p>\n

Detailed SolutionConsider a square of side length 2 m. What is the difference of the ar<\/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":[1110,1102],"class_list":["post-92932","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1110","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nConsider a square of side length 2 m. What is the difference of the ar<\/title>\n<meta name=\"description\" content=\"The correct answer is \u03c0. Let the side length of the square be s = 2 m. The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square. Radius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m. Area of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2. The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square. Diagonal of the square = s * \u221a2 = 2 * \u221a2 m. Radius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m. Area of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2. The difference of the areas = Area of circumscribed circle - Area of inscribed circle Difference = 2\u03c0 m\u00b2 - \u03c0 m\u00b2 = \u03c0 m\u00b2.\" \/>\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\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Consider a square of side length 2 m. What is the difference of the ar\" \/>\n<meta property=\"og:description\" content=\"The correct answer is \u03c0. Let the side length of the square be s = 2 m. The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square. Radius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m. Area of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2. The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square. Diagonal of the square = s * \u221a2 = 2 * \u221a2 m. Radius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m. Area of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2. The difference of the areas = Area of circumscribed circle - Area of inscribed circle Difference = 2\u03c0 m\u00b2 - \u03c0 m\u00b2 = \u03c0 m\u00b2.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:37:02+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":"Consider a square of side length 2 m. What is the difference of the ar","description":"The correct answer is \u03c0. Let the side length of the square be s = 2 m. The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square. Radius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m. Area of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2. The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square. Diagonal of the square = s * \u221a2 = 2 * \u221a2 m. Radius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m. Area of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2. The difference of the areas = Area of circumscribed circle - Area of inscribed circle Difference = 2\u03c0 m\u00b2 - \u03c0 m\u00b2 = \u03c0 m\u00b2.","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\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/","og_locale":"en_US","og_type":"article","og_title":"Consider a square of side length 2 m. What is the difference of the ar","og_description":"The correct answer is \u03c0. Let the side length of the square be s = 2 m. The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square. Radius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m. Area of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2. The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square. Diagonal of the square = s * \u221a2 = 2 * \u221a2 m. Radius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m. Area of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2. The difference of the areas = Area of circumscribed circle - Area of inscribed circle Difference = 2\u03c0 m\u00b2 - \u03c0 m\u00b2 = \u03c0 m\u00b2.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:37:02+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\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/","url":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/","name":"Consider a square of side length 2 m. What is the difference of the ar","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:37:02+00:00","dateModified":"2025-06-01T11:37:02+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is \u03c0. Let the side length of the square be s = 2 m. The inscribed circle is tangent to all four sides of the square. Its diameter is equal to the side length of the square. Radius of the inscribed circle (r_in) = s\/2 = 2\/2 = 1 m. Area of the inscribed circle = \u03c0 * (r_in)\u00b2 = \u03c0 * (1)\u00b2 = \u03c0 m\u00b2. The circumscribed circle passes through all four vertices of the square. Its diameter is equal to the length of the diagonal of the square. Diagonal of the square = s * \u221a2 = 2 * \u221a2 m. Radius of the circumscribed circle (r_circum) = (diagonal)\/2 = (2\u221a2)\/2 = \u221a2 m. Area of the circumscribed circle = \u03c0 * (r_circum)\u00b2 = \u03c0 * (\u221a2)\u00b2 = \u03c0 * 2 = 2\u03c0 m\u00b2. The difference of the areas = Area of circumscribed circle - Area of inscribed circle Difference = 2\u03c0 m\u00b2 - \u03c0 m\u00b2 = \u03c0 m\u00b2.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-a-square-of-side-length-2-m-what-is-the-difference-of-the-ar\/#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":"Consider a square of side length 2 m. 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