Difference between revisions of "2005 AMC 12A Problems/Problem 22"
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Revision as of 11:00, 7 April 2013
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 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |