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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 6 space colon square root of space straight pi end root
Asked by Divyaa | 24 Feb, 2016, 06:43: PM
answered-by-expert Expert Answer
L e t space t h e space r a d i u s space o f space t h e space s p h e r e space b e space apostrophe straight r apostrophe space a n d space s i d e space o f space t h e space c u b e space b e space apostrophe straight a apostrophe. S u r f a c e space o f space t h e space s p h e r e space equals space 4 pi r squared S u r f a c e space o f space t h e space c u b e space equals space 6 straight a squared 6 straight a squared equals 4 pi r squared rightwards double arrow straight a equals square root of fraction numerator 4 pi r 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 V o l u m e space o f space t h e space c u b e space equals space straight a cubed V o l u m e space o f space t h e space s p h e r e space equals space 4 over 3 pi r cubed fraction numerator V o l u m e space o f space t h e space s p h e r e over denominator V o l u m e space o f space t h e space c u b e end fraction equals fraction numerator 4 over 3 pi r cubed over denominator space straight a cubed end fraction equals fraction numerator 4 over 3 pi r 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 pi r 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 Rashmi Khot | 24 Feb, 2016, 07:22: PM

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