My pet snake Earl
"I attach my pet snake, Earl, to one corner of my barn with a leash. The barn is square, with sides of length 10, and the leash has a length of twenty, which wraps around the barn. I would like to make sure that I am being humane to Earl, and would therefore like to know that area of my lawn he can traverse while on the leash. What is this area?"
bron
Solution
We see that since this is at the corner of the barn, the snake is free to travel in a three quarter arc around this point such that it does not intersect the barn. On the corners, we notice that the leash will bend, and basically act as a shorter leash xed at the other two corners. Thus, there is a leash of length 10 for each of two quarter circles, which sum to half of an arc:
- $A$=$\frac{3}{4}\pi 20^2+\frac{1}{2}\pi 10^2$=$350\pi$