Problem:
What is the maximum number of balls of clay with radius 2 that can completely fit inside a cube of side length 6 assuming that the balls can be reshaped but not compressed before they are packed in the cube?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The volume of each ball of radius 2 is . The volume of the cube of side length 6 is . There is room for at most
balls. Because , it follows that
Hence the maximum number of reshaped balls that can completely fit inside the cube is .
The problems on this page are the property of the MAA's American Mathematics Competitions