Question

The surface areas of two spheres are in the ratio `1 : 4`. Find the ratio of their volumes.

Answer 1

Correct Answer - `1 : 8`
`(S_(1))/(S_(2)) = (1)/(4) rArr (4pi R_(1)^(2))/(4pi R_(2)^(2)) = (1)/(4) rArr (R_(1)^(2))/(R_(2)^(2)) = (1)/(4) rArr ((R_(1))/(R_(2)))^(2) = ((1)/(2))^(2) rArr (R_(1))/(R_(2)) = (1)/(2)`
`(V_(1))/(V_(2)) = ((4)/(3) pi (R_(1)^(3)))/((4)/(2)pi (R_(2)^(3))) = (R_(1)^(3))/(R_(2)^(3)) = ((R_(1))/(R_(2)))^(3) = ((1)/(2))^(3) = (1)/(8) rArr V_(1) : V_(2) = 1 : 8`