1. 4.6: Related Rates

4. 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.

5. 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.

6. 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. )

7. 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.

8. As a fundraiser Millwood High is going to be selling tickets for a hot air balloon ride. You have been hired to take pictures of the event for the year book. If you are standing 500 feet from the launch point. How fast is the height of the balloon changing? When the balloon is at 45 degrees, and the change in your viewing angle is 0.14 rad/min.?

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

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

11. 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?

12. 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. 

13. Yes! Its your Fun and Happy Joy Joy Pleasure Time C4.6 #3-39 (multiples of 3), 23, 34, 40. Select a problem from your homework which clearly demonstrates your understanding of Related rates.