In my calculus book, there was a problem as follows.
Find the volume formed by rotating the region $R$, where $R$ is defined as the region enclosed by the function $y=x(1-x)$ and the $y$-axis.
This was straightforward ($V=\frac{\pi}{6}$ units$^2$ by using the "shell" method) until I asked myself:
what about rotating this region about the $x$-axis?
I cannot figure out the volume formed with such a rotation.