1)A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 4 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 8 feet high?

2)Water is pouring into a conical tank at the rate of 8 cubic feet per minute. If the height of the tank is 14 feet and the radius of its circular opening is 5 feet, how fast is the water level rising when the water is 4 feet deep?

  5)As the sun sets behind a 100-foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of pi/3 radians? 

6)Webster City monitors the height of the water in its cylindrical water tank with an automatic recording device. Water is constantly pumped into the tank at the rate of 2200 cubic feet per hour. If the radius of the tank is 20 feet and the water level fell at the rate of 3 feet per hour at 7 A.M., at what rate was water being used exactly at that time?

7)Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more gravel is dumped). How fast is the height of the pile increasing when the pile is 15 feet high?

8)A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. Assume that the snowball remains perfectly spherical as it melts. At what rate is the volume of the snowball decreasing when the diameter is 13 cm?

9)Use differentials to approximate the increase in the surface area of a soap bubble when its radius increases from 4 inches to 4.005 inches.

10)The side of a cube is measured as 11.4 centimeters with a possible error of 0.04 centimeter. Give an estimate for the possible error in the value of the volume of the cube.

 

11)Poiseuille's Law for blood flow says that the volume flowing through an artery is proportional to the fourth power of the radius, that is, V=kR^4. By how much must the radius be increased in order to increase the blood flow by 28%?