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CBSE Class 9 Answered

A sphere and a cube have the same surface area. Show that the ratio of the volume of the sphere to that of the cube is square root of blank end root6:square root of blank end rootstraight pi.
Asked by Varsha | 25 Jan, 2015, 06:15: PM
answered-by-expert Expert Answer
Let space the space radius space of space the space sphere space be space apostrophe straight r apostrophe space and space side space of space the space cube space be space apostrophe straight a apostrophe. Surface space of space the space sphere space equals space 4 πr squared Surface space of space the space cube space equals space 6 straight a squared 6 straight a squared equals 4 πr squared rightwards double arrow straight a equals square root of fraction numerator 4 πr squared over denominator 6 end fraction end root therefore straight a equals straight r square root of fraction numerator 2 straight pi over denominator 3 end fraction end root Volume space of space the space cube space equals space straight a cubed Volume space of space the space sphere space equals space 4 over 3 πr cubed fraction numerator Volume space of space the space sphere over denominator Volume space of space the space cube end fraction equals fraction numerator 4 over 3 πr cubed over denominator space straight a cubed end fraction equals fraction numerator 4 over 3 πr cubed over denominator open parentheses straight r square root of fraction numerator 2 straight pi over denominator 3 end fraction end root close parentheses cubed end fraction equals fraction numerator 4 over 3 πr cubed over denominator straight r cubed begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style square root of begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style end root end fraction equals fraction numerator square root of 2 square root of 3 over denominator square root of straight pi end fraction equals fraction numerator square root of 6 over denominator square root of straight pi end fraction
Answered by Prasenjit Paul | 26 Jan, 2015, 01:24: AM

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