QUESTION 1

A. Gravel is being dumped from a conveyor belt at a rate of 10cubic feet per minute. It forms a pile in the shape of a rightcircular cone whose base diameter and height are always the same.How fast is the height of the pile increasing when the pile is 11feet high? Recall that the volume of a right circular cone withheight h and radius of the base r is given by V= 1/3 pi r^2h. Whenthe pile is 11 feet high, its height is increasing at _______ feetper minute.

B.A street light is at the top of a 15 ft tall pole. A woman 6ft tall walks away from the pole with a speed of 5ft/sec along astraight path. How fast is the tip of her shadow moving along theground when she is 50 ft from the base of the pole? ______ft/secHow fast is the length of her shadow increasing? ______ft/sec

C. Water is leaking out of an inverted conical tank at a rate of0.0087 m^3/min. At the same time water is being pumped into thetank at a constant rate. The tank has height 12 meters and thediameter at the top is 6 meters. If the water level is rising at arate 0.19 m/min when the height of the water is 4.5 meters, findthe rate at which water is being pumped into the tank. Water isbeing pumped in at _____m^3/min.

D. The tip of a 27 foot ladder, leaning against a vertical wall,is slipping down the wall at the rate of 2 feet per second. Howfast is the bottom of the ladder sliding along the ground when thebottom of the ladder is 10 feet away from the base of the ball?

E. A spherical snowball is melting in such a way that itsdiameter is decreasing at rate of 0.2cm/min. At what rate is thevolume of the snowball decreasing when the diameter is 17cm?(Answer is positive number)