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A sphere and a cube has same surface are...

A sphere and a cube has same surface area. Then the ratio of the volume of sphere to cube is

A

`sqrt6 : sqrt pi`

B

`sqrt7 : sqrt pi`

C

`sqrt8 : sqrt pi`

D

`sqrt5 : sqrt pi`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the radius of the sphere be r and the edge of the cube be a
Then
surface area of the sphere = surface area of the cube
`rArr 4 pir^3 = 6a^2 rArr a^2 = 2/3 pi r^2`
` rArr a =r sqrt(2pi)/3`
`therefore` required ratio = volume of shere : volume of cube
`=4/3 pi r^3: a^2 = 4/3pi r^3:2/3pir^3.sqrt((2pi)/3)`
`=2:sqrt((2pi)/3)=sqrt(2):sqrt((pi)/3)=sqrt(6): sqrt(pi)`
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