1990 AHSME Problems/Problem 21

Problem

Consider a pyramid $P-ABCD$ whose base $ABCD$ is square and whose vertex $P$ is equidistant from $A,B,C$ and $D$ . If $AB=1$ and $\angle{APB}=2\theta$ , then the volume of the pyramid is

$\text{(A) } \frac{sin(\theta)}{6}\quad \text{(B) } \frac{cot(\theta)}{6}\quad \text{(C) } \frac{1}{6sin(\theta)}\quad \text{(D) } \frac{1-sin(2\theta)}{6}\quad \text{(E) } \frac{\sqrt{cos(2\theta)}}{6sin(\theta)}$

Solution

$\fbox{E}$

1990 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
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 • 26 • 27 • 28 • 29 • 30
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1990 AHSME Problems/Problem 21

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