If the ratio of curved surface areas of two solid spheres is 16:9, the ratio of their volumes is

Options

A. `64:27`
B. `4:3`
C. `27:64`
D. `3:4`

Explanation

Let the radii of two solid spheres be `r_(1)` units and `r_(2)` units respectively.
`therefore` the curved surface areas of the spheres are `4pi_(1)^(2)" ""sq-units and"" "4pi_(2)^(2) `sq-units respectively
As per question, `4pir_(1)^(2):4pir_(2)^(2)=16:9rArr(4pir_(1)^(2))/(4pir_(1)^(2))=(16)/(9)rArr(r_(1)/(r))^(2)=((4)/3)^(2)rArrr_(1)/r_(2)=(4)/(3)`
`therefore` The ratio of their volumes =`=(4)/(3)pir_(1)^(3):=(4)/(3)pir_(2)^(3)=(4/3pir_(1)^(3))/(4/3pir_(2)^(3))=(r_(1)/(r_(2)))^(3)=((4)/(3))^(3)=(64)/(27)=64:27`
`therefore` is correct.