2008 AMC 12A Problems/Problem 18
Problem
A triangle with sides , , is placed in the three-dimensional plane with one vertex on the positive axis, one on the positive axis, and one on the positive axis. Let be the origin. What is the volume if ?
Solution
WLOG, we let go between the and axes, between and axesCAzxx,y,zOA,OB,OC,x^2+y^2=25y^2+z^2=36z^2+x^2=49x^2 = 30y^2 = 19z^2 = 6\frac{\sqrt{30\cdot 19\cdot 6}}{6}=\sqrt{95}\Rightarrow \boxed{C}$.
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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All AMC 12 Problems and Solutions |