Question

The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is

Options

• 1 : 3

• 1 : 8

• 1 : 9

•  1 : 18

Answer 1

1 : 9
Let the edges of the two cubes be a and b.
Then, ratio of their volumes     ``
Therefore,

`"a"^1 /("b"^3) =1/27 `

`=> (a/b)^3 = (1/3)^3`

`=>"a"/"b"' = 1/3`        

The ratio of their surface areas `=(6"a"^2)/(6"b"^2) `

Therefore,

`(6"a"^2)/(6b^2) = "a2"/"b2"`

`= 1/9 ["since " "a"/"b" = 1/5]`

`=1 : 9`

Hence, the ratio of their surface areas is 1:9.