Difference between revisions of "2018 AMC 10B Problems/Problem 10"
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IMPORTANT: This solution assumed that the parallelepiped is a rectangular prism, which isn't correct. All we know is that each side is a parallelogram, so this solution didn't work. Sorry SS4. | IMPORTANT: This solution assumed that the parallelepiped is a rectangular prism, which isn't correct. All we know is that each side is a parallelogram, so this solution didn't work. Sorry SS4. | ||
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==See Also== | ==See Also== |
Revision as of 19:56, 17 February 2018
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 it b. 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)
Solution 4 (Vectors)
IMPORTANT: This solution assumed that the parallelepiped is a rectangular prism, which isn't correct. All we know is that each side is a parallelogram, so this solution didn't work. Sorry SS4. .
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 |
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