If volumes of two spheres are in the ratio `64 : 27` then the ratio of their surface areas is

Explanation

Let the radii of the given spheres be `R_(1) and R_(2)` respectively and let their volumes be `V_(1) and V_(2)` respectively. Then,
`(V_(1))/(V_(2)) = (64)/(27) rArr ((4)/(3) pi R_(1)^(3))/((4)/(3) pi R_(2)^(3)) = (64)/(27)`
`rArr (R_(1)^(3))/(R_(2)^(3)) = (64)/(27) rArr ((R_(1))/(R_(2)))^(3) = ((4)/(3))^(3) rArr (R_(1))/(R_(2)) = (4)/(3)`...(i)
Let the surface areas of the given sphere be `S_(1) and S_(2)` respectively.
Then, `(S_(1))/(S_(2)) = (4pi R_(1)^(2))/(4pi R_(2)^(2)) = ((R_(1))/(R_(2)))^(2) = (16)/(9)` [using (i)]
Hence, `S_(1) : S_(2) = 16 : 9`