Problem:
Rhombus , with side length 6 , is rolled to form a cylinder of volume 6 by taping to . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let . The base of the cylinder is a circle with circumference 6 , so the radius of the base is . The height of the cylinder is the altitude of the rhombus, which is . Thus the volume of the cylinder is
so .
The problems on this page are the property of the MAA's American Mathematics Competitions