Problem:
A rectangular box is inscribed in a sphere of radius . The surface area of is 384 , and the sum of the lengths of its 12 edges is 112 . What is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the dimensions of be , and . The sum of the lengths of the edges of is , and the surface area of is , so
Each internal diagonal of is a diameter of the sphere, so
.
So and .
Note: There are infinitely many positive solutions of the system , , so there are infinitely many non-congruent boxes meeting the given conditions, but each can be inscribed in a sphere of radius .
The problems on this page are the property of the MAA's American Mathematics Competitions