Difference between revisions of "2008 AMC 12B Problems/Problem 18"
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Revision as of 09:54, 4 July 2013
Problem
A pyramid has a square base and vertex . The area of square is , and the areas of and are and , respectively. What is the volume of the pyramid?
Solution
Let be the height of the pyramid and be the distance from to . The side length of the base is 14. The side lengths of and are and , respectively. We have a systems of equations through the Pythagorean Theorem:
Setting them equal to each other and simplifying gives .
Therefore, , and the volume of the pyramid is .
See also
2008 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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 |
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