2015 AMC 12B Problems/Problem 16
Problem
A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?
Solution
The distance from a corner to the center is 6, and from the corner to the top of the pyramid is 8, so the height is .
The area of the hexagon is
Thus, the volume of the pyramid is
.
See Also
2015 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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