Question
Sun March 08, 2015 By: R K Jha

A sphere and a cube are of same height. The ratio of their volumes is:

(a)3:4   (b)21:11   (c)4:3  (d) 11:21

                 

Expert Reply
Prasenjit Paul
Sun March 08, 2015
L e t space t h e space s i d e space o f space t h e space c u b e space b e space apostrophe a apostrophe comma h e i g h t space o f space t h e space c u b e space equals a V o l u m e space o f space t h e space c u b e comma space V subscript C space equals a cubed  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 r apostrophe H e i g h t space o f space t h e space s p h e r e space equals space 2 r V o l u m e space o f space t h e space s p h e r e comma space V subscript s space equals space 4 over 3 πr cubed  S i n c e space h e i g h t space o f space s p h e r e space a n d space c u b e space i s space s a m e. therefore a equals 2 r V subscript C over V subscript S equals fraction numerator a cubed over denominator 4 over 3 πr cubed end fraction equals fraction numerator left parenthesis 2 r right parenthesis cubed over denominator 4 over 3 πr cubed end fraction equals fraction numerator 8 over denominator begin display style fraction numerator 4 straight pi over denominator 3 end fraction end style end fraction equals 6 over straight pi equals fraction numerator 6 cross times 7 over denominator 22 end fraction equals 21 over 11 V subscript C over V subscript S equals 21 over 11 left parenthesis b right parenthesis space i s space t h e space c o r r e c t space a n s w e r
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