Difference between revisions of "1984 AIME Problems/Problem 9"
(there's clearly a couple of typos in the prob, + solution, box) |
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== See also == | == See also == | ||
{{AIME box|year=1984|num-b=8|num-a=10}} | {{AIME box|year=1984|num-b=8|num-a=10}} | ||
+ | * [[AIME Problems and Solutions]] | ||
+ | * [[American Invitational Mathematics Examination]] | ||
+ | * [[Mathematics competition resources]] |
Revision as of 13:25, 6 May 2007
Problem
In tetrahedron , edge
has length 3 cm. The area of face
is
and the area of face
is
. These two faces meet each other at a
angle. Find the volume of the tetrahedron in
.
Solution
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Position face on the bottom. Since
, we find that
. The height of
forms a
with the height of the tetrahedron, so
. The volume of the tetrahedron is thus
.
See also
1984 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |