{"id":89596,"date":"2025-06-01T10:07:49","date_gmt":"2025-06-01T10:07:49","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89596"},"modified":"2025-06-01T10:07:49","modified_gmt":"2025-06-01T10:07:49","slug":"a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/","title":{"rendered":"A circle is drawn inside a square of length 4 units as shown in the fi"},"content":{"rendered":"

A circle is drawn inside a square of length 4 units as shown in the figure given above. What is the area of the shaded portion?<\/p>\n

[amp_mcq option1=”16-4\u03c0” option2=”16-\u03c0” option3=”4-\u03c0” option4=”4-2\u03c0” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2013<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units.
\nWhen a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units.
\nThe area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units.
\nThe shaded portion is the area of the square minus the area of the inscribed circle.
\nArea of shaded portion = Area of square – Area of circle = 16 – 4\u03c0 square units.
\n<\/section>\n
\nCalculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.
\n<\/section>\n
\nThe formula for the area of a square with side ‘s’ is s\u00b2. The formula for the area of a circle with radius ‘r’ is \u03c0r\u00b2. When a circle is inscribed in a square, the diameter (2r) equals the side (s).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A circle is drawn inside a square of length 4 units as shown in the figure given above. What is the area of the shaded portion? [amp_mcq option1=”16-4\u03c0” option2=”16-\u03c0” option3=”4-\u03c0” option4=”4-2\u03c0” correct=”option1″] This question was previously asked in UPSC CAPF – 2013 Download PDFAttempt Online The figure shows a square with an inscribed circle. The … <\/p>\n

Detailed SolutionA circle is drawn inside a square of length 4 units as shown in the fi<\/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":[1085],"tags":[1467,1102],"class_list":["post-89596","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1467","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA circle is drawn inside a square of length 4 units as shown in the fi<\/title>\n<meta name=\"description\" content=\"The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units. The area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units. The shaded portion is the area of the square minus the area of the inscribed circle. Area of shaded portion = Area of square - Area of circle = 16 - 4\u03c0 square units. Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.\" \/>\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-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A circle is drawn inside a square of length 4 units as shown in the fi\" \/>\n<meta property=\"og:description\" content=\"The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units. The area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units. The shaded portion is the area of the square minus the area of the inscribed circle. Area of shaded portion = Area of square - Area of circle = 16 - 4\u03c0 square units. Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:07:49+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 circle is drawn inside a square of length 4 units as shown in the fi","description":"The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units. The area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units. The shaded portion is the area of the square minus the area of the inscribed circle. Area of shaded portion = Area of square - Area of circle = 16 - 4\u03c0 square units. Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.","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-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/","og_locale":"en_US","og_type":"article","og_title":"A circle is drawn inside a square of length 4 units as shown in the fi","og_description":"The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units. The area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units. The shaded portion is the area of the square minus the area of the inscribed circle. Area of shaded portion = Area of square - Area of circle = 16 - 4\u03c0 square units. Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:07:49+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-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/","name":"A circle is drawn inside a square of length 4 units as shown in the fi","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:07:49+00:00","dateModified":"2025-06-01T10:07:49+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The figure shows a square with an inscribed circle. The side length of the square is given as 4 units. The area of the square is side * side = 4 * 4 = 16 square units. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the diameter of the circle is 4 units. The radius of the circle is half of the diameter, which is 4\/2 = 2 units. The area of the circle is \u03c0 * radius\u00b2 = \u03c0 * (2)\u00b2 = 4\u03c0 square units. The shaded portion is the area of the square minus the area of the inscribed circle. Area of shaded portion = Area of square - Area of circle = 16 - 4\u03c0 square units. Calculating areas of basic geometric shapes like squares and circles, and understanding the relationship between an inscribed circle and its surrounding square, is required.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-circle-is-drawn-inside-a-square-of-length-4-units-as-shown-in-the-fi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"A circle is drawn inside a square of length 4 units as shown in the fi"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89596","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=89596"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89596\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89596"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89596"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}