The volumes of two spheres are in the ratio `64 : 27` and the sum of their radii is `7 cm.` The difference in their total surface area is

Options

A. `38 cm^(2)`
B. `58 cm^(2)`
C. `78 cm^(2)`
D. `88 cm^(2)`

Answer

D

Explanation

Let their radii be x cm and `(7 -x) cm`. Then,
`((4)/(3) pi xx x^(3))/((4)/(3) pi xx (7 -x)^(3)) = (64)/(27) = ((4)/(3))^(3) rArr (x^(3))/((7 -x)^(3)) = ((4)/(3))^(3) rArr ((x)/(7 -x))^(3) = ((4)/(3))^(3)`
`:. (x)/(7 -x) = (4)/(3) rArr 3x = 28 - 4x rArr 7x = 28 rArr x = 4`
So, their radii are 4 cm and 3 cm
Required difference `= 4pi xx (4)^(2) -4pi xx (3)^(2)`