2002 AMC 10A Problems/Problem 19

Problem

Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside of the doghouse that Spot can reach?

$\text{(A)}\ 2\pi/3 \qquad \text{(B)}\ 2\pi \qquad \text{(C)}\ 5\pi/2 \qquad \text{(D)}\ 8\pi/3 \qquad \text{(E)}\ 3\pi$

Solution

Spot can reach a $2\pi-\frac{2\pi}{3}=\frac{4\pi}{3}$ angle of a unit circle; hence he can reach a region with area $\boxed{\frac{2\pi}{3}\Rightarrow\text{(A)}}$ .

2002 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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2002 AMC 10A Problems/Problem 19

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