Volume of a sphere is equal to the volume of a hemisphere. If the radius of the hemisphere is `root3 32` cm, then the radius of the sphere is equal to

Options

A. a) `9 root3 2` cm
B. b) `6 root3 2` cm
C. c) `root3 16` cm
D. d) `root3 64` cm

Answer

D

Explanation

Volume of sphere = `(4)/(3) pi r^(3)`
Volume of hemisphere = `(2)/(3) pi r^(3)`
Now , `(4)/(3) pi r^(3) = (2)/(3) pi r^(3)`
`or (4)/(3) pi^(3) = (2)/(3) ( 3 root32 )^(3)`
or `r^(3) = 2/3 xx 3/4 xx 27 xx 2`
`therefore r =3 `cm