The volume of the two spheres are in the ratio 64: 27 . Find the ratio of their surface areas.

Explanation

Let the radii of two spheres be `r_(1)` and `r_(2)`.
Therefore, their volumes will be `(4)/(3)pi r_(1)^(3)` and `(4)/(3)pi r_(2)^(3)` respectively.
Given that, `((4)/(3)pi r_(1)^(3))/((4)/(3)pi r_(2)^(3)) = (27)/(64) rArr (r_(1)^(3))/(r_(2)^(3))=(27)/(64)`
`rArr ((r_(1))/(r_(2)))^(3) = ((3)/(4))^(3) rArr (r_(1))/(r_(2)) = (3)/(4)`
`rArr (2r_(1))/(2r_(2))=(3)/(4)`
`therefore` The ratio of their diameters = 3 : 4