Clare says, “We know that if we dilate a cube by a factor of `k`, the cube’s volume is multiplied by `k^{3}`. It seems like that must apply to all solids, but I’m not sure how to prove it.” Elena says, “Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by `k^{2}` when we dilate a figure by `k` applies to all shapes, not just rectangles. Can we do something similar here?”

Use Elena’s line of reasoning to argue that for any solid, if it’s dilated by a factor of `k`, the volume is multiplied by `k^{3}`.