Algebra II Pre-AP question adapted from the 2003 AP Calculus AB Free Response question #5
(From College Board website)
The diagram of a coffeepot is displayed below. The radius of the coffee pot is 5 inches and the height is 12 inches. The
coffeepot is completely full at time 0. Volume decreases constantly at a rate of 40 in3 per minute. Let h represent the height
of the coffee in the coffeepot. Use this information and diagram to answer the following questions.
h inches
A. What is the volume of the coffee in the coffeepot after 5 minutes? Show your work.
B. When is the volume of the coffee half the amount of the original volume? Explain your process.
C. Write an equation for the volume as a function of the time. Explain how you developed your equation. What is the
domain? What is the range?
D. Using the equation you developed in part C, find when the coffeepot is empty.
E. Write an equation for the height as a function of the time. Explain how you developed your equation. What is the
domain? What is the range?