Problem:
Two right circular cylinders have the same volume. The radius of the second cylinder is more than the radius of the first. What is the relationship between the heights of the two cylinders?
Answer Choices:
A. $The second height is less than the first.$
B. $The first height is more than the second.$
C. $The second height is less than the first.$
D. $The first height is more than the second.$
E. $The second height is of the first.$
Solution:
Let be the radii and heights of the first and second cylinders, respectively. The volumes are equal, so . Also . Thus . Dividing by yields . Thus the first height is more than the second height.
The problems on this page are the property of the MAA's American Mathematics Competitions