Question

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

Options

• 1 : 3

• 1 : 8

• 1 : 9

•  1 : 18

Answer 1

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is 1 : 9.

Explanation:

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) = "a"^2/"b"^2`

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

`=1 : 9`

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