If the ratio of volumes of two solid spheres is 1:8, the ratio of their curved surface areas is

Options

A. `1:2`
B. `1:4`
C. `1:8`
D. `1:16`

Explanation

Let the radii of the two sphere be `r_(1) "and" r_(2)` units. So the volumes of two spheres are `(4)/(3)pir_(1)^(3)` cubic-units and `(4)/(3)pir_(1)^(3)` cubic-units.
As per questions , `(4)/(3)pir_(1)^(3):(4)/(3)pir_(1)^(3) =1:8 rArr (4/3pir_(1)^(3))/(4/3pir_(2)^(3))=(1)/(8) or,(r_(1)^(3))/(r_(2)^(3)) =(1)/(8)or,(r_(1)/(r_(2)))^(3)=((1)/(2))^(3) or, r^(1)/r^(2)=(1)/(2)`
So, the ratio of their curved surface areas
`=4pir_(1)^(2):4pir_(1)^(2)=(4pir_(1)^(2))/(4pir_(2)^(2))=(r_(1)/(r_(2)))^(2)=((1)/(2))^(2)=(1)/(4)=1:4`
Hence (b) is correct.