Question
A sphere and a cube have equal surface areas . The ratio of the volume of the sphere to that of the cube is :
Answer: Option D
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`4 pi R^2 = 6a^2`
`rArr R^2/r^2 = (3)/(2pi)`
`R/r = sqrt(3)/sqrt( 2pi)`
(Volume of sphere)/( Volume of cube )
=`(4/3 piR^3)/(a^3) = 4/3 pi (R/a)^3 = 4/3 pi (3sqrt(3))/(2 pi sqrt(2 pi)) = 2sqrt(3)/sqrt(2 pi) = sqrt(12)/sqrt(2pi)`
= `sqrt(6)/sqrt(pi)` = `sqrt(6) : sqrt(pi)`
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