A rectangular prism has a base that is 5 cm by 7 cm and a height of 12 cm. If all dimensions are doubled, what happens to the volume?

Hello!

To solve this, first compare the two volumes.

Let's start by first finding the volume of 5*7*12 (length*width*height) which would be 420 cm^3.

Now, find the volume of (5*2) * (7*2) * (12*2) or 10*14*24. This would simplify to 3,360 cm^3.

Now notice, when you double each side, you are basically doing 420*2^3 and 2^3 simplifies to 8. Therefore, when you double the sides, you are multiplying the entire volume of the original dimensions by 8.