Solve each application of operations and composition of functions. Volu...

Solve each application of operations and composition of functions.

Volume of a Sphere The formula for the volume of a sphere is where r represents the radius of the sphere.

(a) Write a function D (r) that gives the volume gained when the radius of a sphere of r inches is increased by 3 inches.

(b) Graph y = D(r) found in part (a), using x for r, in the window [0, 10] by [0, 1500] .

(c) Use your calculator to graphically find the amount of volume gained when a sphere with a 4-inch radius is increased to a 7-inch radius.

(d) Verify your result in part (c) analytically.