Problem:
An inverted cone with base radius and height is full of water. The water is poured into a tall cylinder whose horizontal base has a radius of . What is the height in centimeters of the water in the cylinder?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (A): Let be the height in centimeters of the water in the cylinder. The volume of the water in the cone is . The volume of the water in the cylinder is . The volumes are the same, so . It follows that
OR
The volume of a cylinder is 3 times the volume of a cone with the same base radius and height. Doubling the radius of the cone multiplies the volume by . Therefore the depth of the water in the cylinder will be the depth of the water in the cone, namely centimeters.
The problems on this page are the property of the MAA's American Mathematics Competitions