The ratio of the volumes of two cubes is 1: 27, the ratio of total suface areas of two cubes is

Options

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

Explanation

Let the leghts of equal sides of the two cubes be a and b units repectively . So the volumes of them are `a^3` and `b^3` cubic-units respectively .
As per question `a^3 : b^3 = 1 : 27`
`rArr a^(3)/(b^3)=1/21 rArr (a/b)^3=(1/3)^3rArr a/b = 1/3` [ by taking cube - roots]
`rArr (a/b)^2=(1/3)^2 rArr a^2/b^2 =1 /9 rArr a^2 : b^2 = 1:9`
Hence the ratio of total suface areas of two cubes `= 6a^2=a^2, b^2 =1 : 9`