Question

The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?

Answer 1

Volume of a cube is length * width * height. Because it's a cube, all of these lengths are the same measurement so rather than doing V = l*w*h, we can do one of the measurements cubed, let's call it x.

So Volume = x³. So if we are given the volume, we can the length by doing the cube root. 

∛125 = 5
∛216 = 6

Surface area of a cube = 6x². So now we plug both of these measurements into the formula. 

For 5:

SA = 6(5)² = 6(25) = 150

For 6:

SA = 6(6)² = 6(36) = 216

The ratio of their surface areas is 150:216 or if you simplify it by dividing both by the GCF of 6, 25:36