Difference between revisions of "2008 AMC 12A Problems/Problem 18"
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Revision as of 20:43, 17 February 2008
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
axes
CA
z
x
x,y,z
OA,OB,OC,
x^2+y^2=25
y^2+z^2=36
z^2+x^2=49
x^2 = 30
y^2 = 19
z^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 |