Mr. Stoffregen teaches AP Chemistry. The way a scientist often calculates the volume of a solid object is by putting it in water and finding the volume of the water displaced. As most cats do not like water, it is a funny, not-very-practical way of finding a cat's volume
Mr. Cooper teaches AP Calculus BC. In calculus, integrals can be used to find the area under a curve. If a curve is rotated around an axis, the volume of the object created can also be calculated using integrals.
Mr. Curtis teaches AP Physics. In Physics, a lot of assumptions are made to make solving problems simpler. The cat is assumed to be a sphere, so its volume can be calculated easily.