Question

If the volumes of two cubes are in the ratio 8:125, then the ratio of their surface areas is ______.

Options

• 8:125

• 4:25

• 2:5

• 16:25

Answer 1

If the volumes of two cubes are in the ratio of 8:125, then the ratio of their surface areas is 4:25.

Explanation:

For two cubes, the volume is given by:

V = a³

where a is the side length of the cube.

The surface area of a cube is given by S = 6a²

We are given that the ratio of volumes of two cubes is 8:125.

Let the side lengths of the two cubes be a₁ and a₂.

Since volume is proportional to the cube of side length:

`(a_1/a_2)^3 = 8/125`

Taking the cube root on both sides:

`a_1/a_2 = (root3 8)/(root3 125) = 2/5`

Since the surface area is proportional to the square of the side length:

`(S_1/S_2) = (a_1/a_2)^2`

= `(2/5)^2`

= `4/25`

= 4:25