1. 4.6: Related Rates Greg Kelly, Hanford High School, Richland, Washington

2. Problem 10 This presentation was created by Greg Kelly (see my Resources page for more information). I simply edited it to make it more animated for you. Do not believe that test questions will be exactly like the practice tests or these examples. Any question is fair to ask. The more you study the better you will do. See pages 820 – 826 and 835 – 836 for more problems. You will need to refer to page A–1 in the back of your book. It has formulas and sketches that you might need.

3. First, a review problem: Consider a sphere of radius 10cm. If the radius changes 0.1cm (a very small amount) how much does the volume change? The volume would change by approximately.

4. Now, suppose that the radius is changing at an instantaneous rate of 0.1 cm/sec. (Possible if the sphere is a soap bubble or a balloon.) The sphere is growing at a rate of. Note: This is an exact answer, not an approximation like we got with the differential problems.

5. Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping? Find ( r is a constant.) (We need a formula to relate V and h. )

6. Steps for Related Rates Problems: 1. Draw a picture (sketch). 2. Write down known information. 3. Write down what you are looking for. 4. Write an equation to relate the variables. 5. Differentiate both sides with respect to t. 6. Evaluate.

7. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

8. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

9. B A Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later?

10. B A Truck Problem: How fast is the distance between the trucks changing 6 minutes later? Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. 