Let’s take a puppy and compare it with a full-grown dog that is four times bigger. I am assuming that all linear dimensions of the bigger dog are four times larger than that of the puppy—its height, its length, the length and the thickness of its legs, the width of its head, everything. If that is the case, then the volume (and thus the mass) of the bigger dog is about sixty-four times that of the puppy.One way to see this is by taking a cube with sides a, b, and c. The volume of this cube is a × b × c. When you make all sides four times larger, the volume becomes 4a × 4b × 4c, which is 64abc. If we express this a bit more mathematically, we can say that the volume (thus the mass) of the mammal is proportional to its length to the third power. If the bigger dog is four times larger than the puppy, then its volume should be about 4 cubed (43) times larger, which is 64. So, if we call the length of the femur “l,” then by comparing mammals of different size, their mass should be roughly proportional to l cubed (l3).Okay, that’s mass.
