Position of a piston The distance between the head of a piston and the end of a cylindrica...

Position of a piston The distance between the head of a piston and the end of a cylindrical chamber is given by , for t ≥ 0 (measured in seconds). The radius of the cylinder is 4 cm.

a. Find the volume of the chamber, for t ≥ 0.

b. Find the rate of change of the volume V′(t), for t ≥ 0.

c. Graph the derivative of the volume function. On what intervals is the volume increasing? Decreasing?