Solids From Solids

Real objects are often two solids joined together: a pencil is a cylinder with a cone on top, a silo is a cylinder with a dome. The volume of the whole is the volumes of the parts added up.

Here a cone stands on a cylinder and they share the same circle, radius 3. The cylinder holds $\pi\cdot {3}^{2}\cdot 5 = 45\cdot \pi$ and the cone $\frac{1}{3}\cdot \pi\cdot {3}^{2}\cdot 4 = 12\cdot \pi$, so the whole solid holds $45\cdot \pi+12\cdot \pi = 57\cdot \pi$.

The shared circle is the clue: one radius serves both parts. Find each part with its own rule, then add.