The surface areas of two spheres are in the ratio `16 : 9` . The ratio of their volumes is

Options

A. `64 : 27`
B. `16 : 9`
C. `4 : 3`
D. `16^(3) : 9^(3)`

Answer

A

Explanation

`(4pi R^2)/(4 pi r^2)=16/9 rArr (R^2)/(r^2)=16/9 rArr R/r = sqrt(16)/(9)= 4/3`
`rArr (R^3)/(r^3)=(4^3)/(3^3)=(64)/(27)rArr (4/3piR^3)/(4/3pir^3)=64/27`