Two cubes have their volume in the ratio `1 : 27`. The ratio of their surface areas is

Options

A. `1 : 3`
B. `1 : 8`
C. `1 : 9`
D. `1 : 18`

Answer

C

Explanation

`(a^(3))/(b^(3)) = (1)/(27) rArr ((a)/(b))^(3) = ((1)/(3))^(3) rArr (a)/(b) = (1)/(3)`
`rArr (a^(2))/(b^(2)) = ((1)/(3))^(2) = (1)/(9) rArr (6a^(2))/(6b^(2)) = (6 xx 1)/(6 xx 9) = (1)/(9)`
`:.` required ratio `= 1 : 9`