1. As a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4 cubic inches per second. At what rate is the radius increasing when the radius is 1 inch?
2. Two cars leave at an intersection at 1 pm. The first car is traveling east at 45 miles/hour while the second is traveling north at 60 miles/hour. How fast is the distance between the cars increasing at 3 pm?
3. A truck is dumping sand into a conical pile at the rate of 30 cubic foot/second, and in such a way that the height of the piles is always equal to twice the radius. At what rate is the height increasing when the sand pile has a volume of 300 cubic ft?
4. A conical paper cup has a height of 6 inches, while the radius of the circular opening at the top is 2 inches. The cup was initially filled with water but there is a leak at the bottom. At what rate is water out of the cup when the water level in the cup is 3 inches, and is dropping at the rate of 1 inch per minute?
Thanks for any help.