The volume of one cube is 125 times the volume of another cube. How many times is the surface area

The volume of one cube is 125 times the volume of another cube. How many times is the surface area of the first cube greater than the surface area of the second cube?

Let the side of the smaller cube be equal to k, then the volume of this cube is equal to k ^ 3. The volume of the larger cube is 125 * k ^ 3. Then you can find its side by volume, as the cubic root of 125 * k ^ 3 = 5 * k.

The surface area of the smaller cube is 6 * k ^ 2.

The area of a large cube is 6 * (5 * k) ^ 2 = 6 * 25 * k ^ 2 = 150 * k ^ 2.

Now you can determine how many times the surface area of the first is greater than the same area of the second cube.

(150 * k ^ 2) / (6 * k ^ 2) = 25 (times).

That is, this area is larger, how much larger is the side in the square.