Problem 457

Given $s_{1}=s_{2}=0, s_{0}=\pi a b, h=2 c$,
$$\therefore V=\frac{2 c}{6}(0+4 \pi a b+0)=\frac{4}{3} \pi a b c \text {. }$$

In particular, when $c=b$, we get the
volume of an ellipsoid of revolution (Example 2)
When $a=b=c=R$, we get
$$V_{\text {sphere }}=\frac{4}{3} \pi R^{3} \text { . }$$

Using the formula for the volume of a frustum
we can also calculate the volume of solids of revolution
formed by rotating certain transcendental curves around
coordinate axes.