1990 AHSME Problems/Problem 21
Problem
Consider a pyramid whose base
is square and whose vertex
is equidistant from
and
. If
and
, then the volume of the pyramid is
Solution
As the base has area , the volume will be one third of the height. Drop a line from
to
, bisecting it at
.
Then
, so
. Therefore
.
Now turning to the dotted triangle, by Pythagoras, the square of the pyramid's height is and after taking the square root and dividing by three, the result is
See also
1990 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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