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 it's 12 edges is 112. What is ?
Solution
The box P has dimensions , , and . Therefore,
Now we make a formula for . Since the diameter of the sphere is the space diagonal of the box,
We square :
We get that
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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All AMC 12 Problems and Solutions |
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