The region enclosed by the graphs of $y=x^2$ and $y=4$ is revolved about the line $x=3$. What is the volume of the resulting solid?

Core Concept

Horizontal slices are washers with outer radius $3+\sqrt{y}$ and inner radius $3-\sqrt{y}$. The volume is $\pi\int_0^4((3+\sqrt{y})^2-(3-\sqrt{y})^2)\,dy=\pi\int_0^4 12\sqrt{y}\,dy=12\pi\cdot\frac{16}{3}=64\pi$.