Question

A tin man has a head that is a cylinder with a cone on top. The height of the cylinder is 12 inches and the height of the cone is 6 inches. The radius of both the cylinder and the cone is 4 inches. What is the volume of the tin man's head in terms of pi?

Answer 1

First find the volume of the cylinder, then the volume of the cone, and after you can add the two volumes.

Cylinder:
V = π r^2 h
h = 12 inches
r = 4 inches
V = π(4^2)(12)
V = 192π

Cone:
V = 1/3 π r^2 h
h = 6 inches
r = 4 inches
V = 1/3 π (4^2)(6)
V = 32π

Now adding the two volumes, 192π + 32π = 224π cubic inches