Answer
see explanation
Work Step by Step
It helps to visualize something like toilet paper
Thickness is $R-r (outside - inside)$
Average radius is $\frac{R+r}{2}$ (average of two)
formula given is $ V=\pi{R}^{2}h-\pi{r}^{2}h$
Factor out common factor $ \pi{h}$
$V= \pi{h}(R^{2}-r^{2})$
Use special product formula [ $A^{2}-B^{2} =(A-B)(A+B)$]
$V=\pi{h}(R-r)(R+r)$
Remember (R-r) is the thickness
(R+r) is 2 x average radius
h is height
So we have $V= \pi(height)(thickness)(2average Radius)$
Rearrange
$ V= 2\pi*average Radius*height*thickness$
