Problem 10

Explanation

Finding the Side Length Ratio

The volume of a cube ($V$) is directly proportional to the cube of its side length ($s$). Given that the volume ratio is $1 : 27$.

So, the ratio of the side lengths of the two cubes is $1 : 3$.

Finding the Surface Area Ratio

The surface area of a cube ($L$) is directly proportional to the square of its side length.

Thus, the ratio of the surface areas of the two cubes is $1 : 9$.