The radius r of a sphere is increasing at a rate of 2 inches per minute.  Find the rate of change of the volume when r=6 inches.

All edges of a cube are expanding at a rate of 3 centimeters per second.  How fast is the volume changing each edge is 1 centimeter.

In a cone, find the rate of change of the volume if dr/dt is 2 inches per minute and the height is 3r when the radius is 6.

A conical tank is 10 feet across the top and 12 feet deep.  If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water if 8 feet deep.

A construction worker pulls a five meter plank up the side of a building under construction by means of a rope tied to one end of the plank.  Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of .15 meters per second.  How fast is the end of the plank sliding along the ground when when it is 2.5 meters from the wall of the building?

A boat is being pulled into dock by means of a winch 12 feet above the deck of the boat. The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out.