Related Rates Homework

Read through this tutorial on related rates problems. It's a lot to read but it's worth your time. The beginning will take you through the general steps to take in solving related rates problems, then there are several examples that have animations to show you what is changing in the problem and how.

Here is another tutorial with animations and a problem set. You can do as many questions from the problem set as you like. You may also want to try the first 5 questions here. Answers are provided so see if you can solve them without looking at the answers. ;-)

All of that is just too get extra help if you need it. This is your homework:

The Three Questions:

(1) As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the rate at which the area of one side is changing when the diameter is 30 centimeters.

Answer: 0.15π cm/min


(2) A stone is dropped into a lake, causing circular waves whose radii increase at a constant rate of 0.5 m/sec. At what rate is the circumference of a wave changing when its radius is 4 meters?

Answer: π m/sec


(3) The ends of a water trough 8 feet long are equilateral triangles whose sides are 2 feet long. If water is being pumped into the trough at a rate of 5 ft³/min, find the rate at which the water level is rising when the depth of the water is 8 inches.

Answer: (15/32)√(3) ft/min