A sculptor uses a constant volume of modeling clay to form a cylinder with a large height and a relatively small radius. The clay is molded in such a way that the height of the clay increases as the radius decreases, but it retains its cylindrical shape. At time t=c, the height of the clay is 8 inches, the radius of the clay is 3 inches, and the radius of the clay is decreasing at a rate of 1/2 inch per minute (a) At time t=c, at what rate is the area of the circular cross section of the clay decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure.

(b) At time t=c , at what rate is the height of the clay increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V=πr2h .)

(c) Write an expression for the rate of change of the radius of the clay with respect to the height of the clay in terms of height h and radius r.