2018 AMC 10B Problems/Problem 10
Problem
In the rectangular parallelpiped shown, = , = , and = . Point is the midpoint of . What is the volume of the rectangular pyramid with base and apex ?
Solution 1
Consider the cross-sectional plane and label its area . Note that the volume of the triangular prism that encloses the pyramid is , and we want the rectangular pyramid that shares the base and height with the triangular prism. The volume of the pyramid is , so the answer is . (AOPS12142015)
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.