Problem
4. (15 points) Find the volume generated by rotating area $\mathrm{A}$ about the $\mathrm{x}$-axis.
Solution
Step 1 ：The resulting solid is the union of two cylinders: one whose radius is 5 units and whose height is 1 unit, and the other whose radius is 2 units and whose height is 3 units.
Step 2 ：The sum of these volumes is \(\pi(5)^2(1)+\pi(2)^2(3)\).
Step 3 ：So the volume of the resulting solid is \(\boxed{37\pi}\) cubic units.
