1. Olympic National Park, Washington Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007 3.9: Related Rates

2. The sphere is growing at a rate of. Consider a sphere whose radius is changing at a rate of 0.1 cm/sec. How fast is the volume changing? Begin with a primary equation. Differentiate with respect to time. Substitute known values. Simplify,

3. Water is draining from a cylindrical tank at 3 liters/second. The tank has a radius of 20 ft. How fast is the surface dropping?

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

5. 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?

6. 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. 

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