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

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

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.