calculus 1

MAT1214 Takehome Chapter 3 Section 10 Related Rates NAME: ____________________________________

NOTE: You must SHOW your work to receive credit for the problems.

1. A boat is being pulled toward a dock as shown in the figure to the

right. If the rope is being pulled in at a rate of 2 feet per second, how

fast is the distance between the dock and the boat decreasing when it

is 5 feet from the dock? (10 points)

2. A piston is seated at the top of a cylindrical chamber with radius 5 centimeters when it

starts moving into the chamber at a constant speed of 8 centimeters per second. What is

the rate of change of the volume of the cylinder when the piston is 6 centimeters from

the base of the chamber? (30 points)

3. Water is drained out of an inverted cone, having the dimensions in the

picture shown. If the water level drops at 3 feet per minute, at what rate is

the water in cubic feet per minute, draining from the tank when the water

depth is 4 feet? (30 points)