2002 AMC 10A Problems/Problem 19
Contents
[hide]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?
Solution
Part of what Spot can reach is of a circle with radius 2, which gives him . He can also reach two parts of a unit circle, which combines to give . The total area is then , which gives .
Note
We can clearly see that the area must be more than , and the only such answer is .
Video Solution
https://www.youtube.com/watch?v=lkk3SAjsPaI ~David
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
See Also
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.