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 × 3^2 × 5 = 45×pi and the cone 1/3 × pi × 3^2 × 4 = 12×pi, so the whole solid holds 45×pi + 12×pi = 57×pi.

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