Teacher Guide and Answer Key, Middle School Activity 3
Based on AP* Calculus AB Problem 5, 1995
This is a good Pre-AP* worksheet because it expects students to combine many different concepts and skills responding to a single scenario, much like an AP* test question does. Students have to be able to interpret the questions and select appropriate strategies. There are opportunities to discuss things pertaining to units and the different forms that the answers may take.
Oil is being stored in a conical storage tank having a radius of 6 feet and a height of 15 feet.
1. What is the capacity of the storage tank?
2. What is the ratio of the tank radius to its depth?
3. If the height of the oil in the tank is 10 ft, what is the radius of the oil in the tank?
4. What is the volume of oil in the tank?
5. What is the ratio of the volume of the oil to the capacity of the tank?
6. What is the ratio of the radius of the oil to the radius of the tank?
7. What is the relationship between your answers to #5 and #6?
8. What is the area of the surface of the oil in the tank?
9. If the oil currently in the tank is pumped out at a rate of 2 cubic feet/minute, how long will it take to empty the tank?
10. If the oil currently in the tank is pumped into another tank that is a right cylinder with a radius of 8 feet and a depth of 12 feet, what will be the depth of the oil in this new tank?
