{"id":93122,"date":"2025-06-01T11:42:18","date_gmt":"2025-06-01T11:42:18","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93122"},"modified":"2025-06-01T11:42:18","modified_gmt":"2025-06-01T11:42:18","slug":"a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/","title":{"rendered":"A solid metallic sphere of 2 cm radius is melted and converted to a cu"},"content":{"rendered":"

A solid metallic sphere of 2 cm radius is melted and converted to a cube. The side of the cube is approximately equal to :<\/p>\n

[amp_mcq option1=”2.4 cm” option2=”2.8 cm” option3=”3.2 cm” option4=”3.6 cm” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nWhen a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant.
\nRadius of the sphere (r) = 2 cm.
\nVolume of the sphere (Vsphere<\/sub>) = (4\/3)\u03c0r\u00b3.
\nVsphere<\/sub> = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3.
\nLet the side of the cube be ‘s’ cm.
\nVolume of the cube (Vcube<\/sub>) = s\u00b3.
\nSince the volume is conserved, Vcube<\/sub> = Vsphere<\/sub>.
\ns\u00b3 = (32\/3)\u03c0.
\nTo find ‘s’, we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0].
\nUsing the approximate value of \u03c0 \u2248 3.14159:
\n(32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3.
\ns \u2248 \u00b3\u221a33.51 cm.
\nLet’s evaluate the cube of the given options:
\nA) (2.4)\u00b3 \u2248 13.824
\nB) (2.8)\u00b3 \u2248 21.952
\nC) (3.2)\u00b3 \u2248 32.768
\nD) (3.6)\u00b3 \u2248 46.656
\nThe value 3.2\u00b3 = 32.768 is closest to 33.51.
\n<\/section>\n
\n– The volume of the material is conserved during melting and recasting.
\n– Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3.
\n– Formula for the volume of a cube: V = s\u00b3.
\n– Solve for the side ‘s’ by equating the volumes and taking the cube root.
\n<\/section>\n
\nThe value of \u03c0 is an irrational number, so the exact value of ‘s’ is \u00b3\u221a[(32\/3)\u03c0]. The question asks for an approximate value, so we use the numerical value of \u03c0. The calculation shows that 3.2 cm is the closest approximation among the given options.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A solid metallic sphere of 2 cm radius is melted and converted to a cube. The side of the cube is approximately equal to : [amp_mcq option1=”2.4 cm” option2=”2.8 cm” option3=”3.2 cm” option4=”3.6 cm” correct=”option3″] This question was previously asked in UPSC CISF-AC-EXE – 2022 Download PDFAttempt Online When a solid metallic sphere is melted … <\/p>\n

Detailed SolutionA solid metallic sphere of 2 cm radius is melted and converted to a cu<\/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":[1108,1102],"class_list":["post-93122","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA solid metallic sphere of 2 cm radius is melted and converted to a cu<\/title>\n<meta name=\"description\" content=\"When a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant. Radius of the sphere (r) = 2 cm. Volume of the sphere (Vsphere) = (4\/3)\u03c0r\u00b3. Vsphere = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3. Let the side of the cube be 's' cm. Volume of the cube (Vcube) = s\u00b3. Since the volume is conserved, Vcube = Vsphere. s\u00b3 = (32\/3)\u03c0. To find 's', we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0]. Using the approximate value of \u03c0 \u2248 3.14159: (32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3. s \u2248 \u00b3\u221a33.51 cm. Let's evaluate the cube of the given options: A) (2.4)\u00b3 \u2248 13.824 B) (2.8)\u00b3 \u2248 21.952 C) (3.2)\u00b3 \u2248 32.768 D) (3.6)\u00b3 \u2248 46.656 The value 3.2\u00b3 = 32.768 is closest to 33.51. - The volume of the material is conserved during melting and recasting. - Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3. - Formula for the volume of a cube: V = s\u00b3. - Solve for the side 's' by equating the volumes and taking the cube root.\" \/>\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-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A solid metallic sphere of 2 cm radius is melted and converted to a cu\" \/>\n<meta property=\"og:description\" content=\"When a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant. Radius of the sphere (r) = 2 cm. Volume of the sphere (Vsphere) = (4\/3)\u03c0r\u00b3. Vsphere = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3. Let the side of the cube be 's' cm. Volume of the cube (Vcube) = s\u00b3. Since the volume is conserved, Vcube = Vsphere. s\u00b3 = (32\/3)\u03c0. To find 's', we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0]. Using the approximate value of \u03c0 \u2248 3.14159: (32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3. s \u2248 \u00b3\u221a33.51 cm. Let's evaluate the cube of the given options: A) (2.4)\u00b3 \u2248 13.824 B) (2.8)\u00b3 \u2248 21.952 C) (3.2)\u00b3 \u2248 32.768 D) (3.6)\u00b3 \u2248 46.656 The value 3.2\u00b3 = 32.768 is closest to 33.51. - The volume of the material is conserved during melting and recasting. - Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3. - Formula for the volume of a cube: V = s\u00b3. - Solve for the side 's' by equating the volumes and taking the cube root.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:42:18+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 solid metallic sphere of 2 cm radius is melted and converted to a cu","description":"When a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant. Radius of the sphere (r) = 2 cm. Volume of the sphere (Vsphere) = (4\/3)\u03c0r\u00b3. Vsphere = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3. Let the side of the cube be 's' cm. Volume of the cube (Vcube) = s\u00b3. Since the volume is conserved, Vcube = Vsphere. s\u00b3 = (32\/3)\u03c0. To find 's', we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0]. Using the approximate value of \u03c0 \u2248 3.14159: (32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3. s \u2248 \u00b3\u221a33.51 cm. Let's evaluate the cube of the given options: A) (2.4)\u00b3 \u2248 13.824 B) (2.8)\u00b3 \u2248 21.952 C) (3.2)\u00b3 \u2248 32.768 D) (3.6)\u00b3 \u2248 46.656 The value 3.2\u00b3 = 32.768 is closest to 33.51. - The volume of the material is conserved during melting and recasting. - Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3. - Formula for the volume of a cube: V = s\u00b3. - Solve for the side 's' by equating the volumes and taking the cube root.","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-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/","og_locale":"en_US","og_type":"article","og_title":"A solid metallic sphere of 2 cm radius is melted and converted to a cu","og_description":"When a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant. Radius of the sphere (r) = 2 cm. Volume of the sphere (Vsphere) = (4\/3)\u03c0r\u00b3. Vsphere = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3. Let the side of the cube be 's' cm. Volume of the cube (Vcube) = s\u00b3. Since the volume is conserved, Vcube = Vsphere. s\u00b3 = (32\/3)\u03c0. To find 's', we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0]. Using the approximate value of \u03c0 \u2248 3.14159: (32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3. s \u2248 \u00b3\u221a33.51 cm. Let's evaluate the cube of the given options: A) (2.4)\u00b3 \u2248 13.824 B) (2.8)\u00b3 \u2248 21.952 C) (3.2)\u00b3 \u2248 32.768 D) (3.6)\u00b3 \u2248 46.656 The value 3.2\u00b3 = 32.768 is closest to 33.51. - The volume of the material is conserved during melting and recasting. - Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3. - Formula for the volume of a cube: V = s\u00b3. - Solve for the side 's' by equating the volumes and taking the cube root.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:42:18+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-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/","name":"A solid metallic sphere of 2 cm radius is melted and converted to a cu","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:42:18+00:00","dateModified":"2025-06-01T11:42:18+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"When a solid metallic sphere is melted and converted into a cube, the volume of the material remains constant. Radius of the sphere (r) = 2 cm. Volume of the sphere (Vsphere) = (4\/3)\u03c0r\u00b3. Vsphere = (4\/3) * \u03c0 * (2 cm)\u00b3 = (4\/3) * \u03c0 * 8 cm\u00b3 = (32\/3)\u03c0 cm\u00b3. Let the side of the cube be 's' cm. Volume of the cube (Vcube) = s\u00b3. Since the volume is conserved, Vcube = Vsphere. s\u00b3 = (32\/3)\u03c0. To find 's', we take the cube root: s = \u00b3\u221a[(32\/3)\u03c0]. Using the approximate value of \u03c0 \u2248 3.14159: (32\/3)\u03c0 \u2248 (10.6667) * 3.14159 \u2248 33.51 cm\u00b3. s \u2248 \u00b3\u221a33.51 cm. Let's evaluate the cube of the given options: A) (2.4)\u00b3 \u2248 13.824 B) (2.8)\u00b3 \u2248 21.952 C) (3.2)\u00b3 \u2248 32.768 D) (3.6)\u00b3 \u2248 46.656 The value 3.2\u00b3 = 32.768 is closest to 33.51. - The volume of the material is conserved during melting and recasting. - Formula for the volume of a sphere: V = (4\/3)\u03c0r\u00b3. - Formula for the volume of a cube: V = s\u00b3. - Solve for the side 's' by equating the volumes and taking the cube root.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-solid-metallic-sphere-of-2-cm-radius-is-melted-and-converted-to-a-cu\/#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 solid metallic sphere of 2 cm radius is melted and converted to a cu"}]},{"@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\/93122","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=93122"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93122\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}