Difference between revisions of "2002 AMC 10A Problems/Problem 19"

(hm)
(No difference)

Revision as of 23:27, 26 December 2008

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 $\boxed{\frac{2\pi}{3}\Rightarrow\text{(A)}}$.

See Also

2002 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
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
All AMC 10 Problems and Solutions
Invalid username
Login to AoPS