Question

The volumes of two cubes are in the ratio 8 : 27. Find the ratio of their surface areas.

Answer 1

Let the edges of cubes be a and b.

As, 

`"Volume of the first cube"/"Volume of the second cybe" = 8/27`

`=> a^3/b^3 = 8/27`

`=> a/b = root(3)(8/27)`

`=>a/b = 2/3`          .................(i)

Now,

The ratio of the surface areas of the cubes `= "Surface area of the first cube"/"Surface area of the second cube"`

`= "6a"^2/"6b"^2`

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

`=(2/3)^2`          [Using (i)]

`=4/9`

So, the ratio of the surface areas of the given cubes is 4 : 9.