triangle is not constant even u 13. Volume The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rates of change of the volume when r = 9 inches and r = 36 inches. (b) Explain why the rate of change of the volume of the sphere is not constant even though dr / dt is constant. 14. Volume A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters? 15. Volume All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is (a) 2 centimeters and (b) 10 centimeters? 16. Surface Area All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface area changing when each edge is (a) 2 centimeters and (b) 10 centimeters? 17. Volume At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high? (Hint: The formula for the volume of a cone is V = > mr2h.)