Problem:
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are in diameter and high. Felicia buys cat food in cylindrical cans that are in diameter and high. What is the ratio of the volume of one of Alex's cans to the volume of one of Felicia's cans?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Felicia's diameter is twice as much as Alex's, which means that her radius is also twice as much. Recall that the formula for the area of a circle is . If the radius is doubled, then the area is quadrupled. This means that the base of Felicia's can has times the area as the base of Alex's can. We also see that Alex's can is twice as tall as Felicia's can. The formula for the volume of a can is the base times the height. Using this formula, we see that Felicia's can will have twice the volume of Alex's can since .
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions