{"id":648378,"date":"2023-06-27T00:42:04","date_gmt":"2023-06-26T19:12:04","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-cube-of-side-4-cm-is-cut-into-1-cm-cubes-what-is-the-ratio-of-the-surface-areas-of-the-original-cubes-and-cut-out-cubes\/"},"modified":"2025-06-20T14:28:20","modified_gmt":"2025-06-20T08:58:20","slug":"a-cube-of-side-4-cm-is-cut-into-1-cm-cubes-what-is-the-ratio-of-the-surface-areas-of-the-original-cubes-and-cut-out-cubes","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/a-cube-of-side-4-cm-is-cut-into-1-cm-cubes-what-is-the-rati\/","title":{"rendered":"A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?","custom_permalink":"question\/mathematics\/a-cube-of-side-4-cm-is-cut-into-1-cm-cubes-what-is-the-rati\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:normal\"><span>A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"1: 2","correct":false},{"option":"1: 3","correct":false},{"option":"1: 4","correct":true},{"option":"1: 6<span>&nbsp;<\/span>","correct":false}],"solution":"<span>Given that,<\/span><br><span>A cube of side 4 cm is cut into 1 cm cubes.<\/span><br><span>We know,<\/span><br><span>Volume of cube is given by a\u00b3. <\/span><br><span>Surface area of cube is given by 6a\u00b2, where a is the edge length of cube.<\/span><br><span>Therefore, the surface area will be,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>Surface&nbsp;area<\/m:mtext><m:mo>=<\/m:mo><m:mtext>6<\/m:mtext><m:mo>\u00d7<\/m:mo><m:msup>\r\n      <m:mn>4<\/m:mn>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>Surface&nbsp;area<\/m:mtext><m:mo>=<\/m:mo><m:mtext>9<\/m:mtext><m:mn>6<\/m:mn><m:mi>c<\/m:mi><m:msup>\r\n      <m:mi>m<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>Now, volume of original cube with volume of l new cut out cube.<\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mtext>Number&nbsp;of&nbsp;cubes&nbsp;=&nbsp;<\/m:mtext><m:mfrac>\r\n      <m:mrow>\r\n       <m:msup>\r\n        <m:mn>4<\/m:mn>\r\n        <m:mn>3<\/m:mn>\r\n       <\/m:msup>\r\n       <\/m:mrow>\r\n      <m:mrow>\r\n       <m:msup>\r\n        <m:mn>1<\/m:mn>\r\n        <m:mn>3<\/m:mn>\r\n       <\/m:msup>\r\n       <\/m:mrow>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>Number&nbsp;of&nbsp;cubes&nbsp;=&nbsp;<\/m:mtext><m:mn>64<\/m:mn>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>The surface area will be,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>A=&nbsp;6&nbsp;<\/m:mtext><m:mo>\u00d7<\/m:mo><m:msup>\r\n      <m:mn>1<\/m:mn>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>A=&nbsp;6&nbsp;<\/m:mtext><m:mi>c<\/m:mi><m:msup>\r\n      <m:mi>m<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>Multiply with number of cubes (64) to find total surface area of cut out cubes,<\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>Surface&nbsp;area<\/m:mtext><m:mo>=<\/m:mo><m:mtext>64&nbsp;<\/m:mtext><m:mo>\u00d7<\/m:mo><m:mtext>&nbsp;6<\/m:mtext>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mtext>Surface&nbsp;area<\/m:mtext><m:mo>=<\/m:mo><m:mtext>3<\/m:mtext><m:mn>84<\/m:mn><m:mi>c<\/m:mi><m:msup>\r\n      <m:mi>m<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msup>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>Now, the ratio of surface area of original cube to cut out cubes is,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mn>96<\/m:mn><m:mo>:<\/m:mo><m:mn>384<\/m:mn>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mn>1<\/m:mn><m:mo>:<\/m:mo><m:mn>4<\/m:mn>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>Hence, the required ratio is 1:4.<\/span><br><span>Therefore, option 3 is correct.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A cube of side 4 cm is cut into 1 cm cubes. 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