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
axes,
between
and
axes. Let
be
respectively. By the Pythagorean Theorem,
,
,
. Thus,
,
, and
. Thus the volume of the tetraehdron is
.
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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 12 Problems and Solutions |