2005 AMC 12A Problems/Problem 22
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 ?
Solution
Box P has dimensions , , and . Its surface area is while the sum of all its edges is
The diameter of the sphere is the space diagonal of the prism, which is Notice that so the diameter is . The radius is half of the diameter, so
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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