Answer
(a) $\pi h(R+r)(R-r)$
(b) $\ 2 \pi h \frac{R+r}{2}(R-r)\ = \pi h(R+r)(R-r)$
Work Step by Step
(a)
when factored, $$\pi R^{2}h - \pi r^{2}h
= \pi h(R+r)(R-r)$$
(b)
Average Radius: $\frac{R+r}{2}$
Thickness of the shell: $R-r$
$2\pi h (average)(thickness) = \pi h(R+r)(R-r)$$
$$\ 2 \pi h \frac{R+r}
{2}(R-r)\ = \pi h(R+r)(R-r)$
