Example 5

Find the mass of a sphere of radius c whose density is equal to the distance from the surface. The sphere is shown in Figure 12.7.20.

Figure 12.7.20

Put the center at the origin. The sphere is then given by

0 ≤ θ ≤ 2n, 0 ≤ φ ≤ n, 0 ≤ ρ ≤ c.

The density at (θ, φ, ρ) is

density = c - ρ.

The mass is