Difference between revisions of "1984 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
− | In [[tetrahedron]] <math> | + | In [[tetrahedron]] <math>ABCD</math>, [[edge]] <math>AB</math> has length 3 cm. The area of [[face]] <math>ABC</math> is <math>15\mbox{cm}^2</math> and the area of face <math>ABD</math> is <math>12 \mbox { cm}^2</math>. These two faces meet each other at a <math>30^\circ</math> angle. Find the [[volume]] of the tetrahedron in <math>\mbox{cm}^3</math>. |
== Solution == | == Solution == | ||
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* [[American Invitational Mathematics Examination]] | * [[American Invitational Mathematics Examination]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
+ | |||
+ | [[Category:Intermediate Geometry Problems]] |
Revision as of 09:37, 18 October 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
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 |