6. A man, standing on a lawn, is wearing a circular sombrero of radius 3 feet. Unfortunately, the hat blocks the sunlight so effectively that the grass directly under it dies instantly. If the man walks in a circle of radius 5 feet, what area of dead grass will result?
Solution: $60 \pi \mathrm{ft}^{2}$ Let $O$ be the center of the man's circular trajectory. The sombrero kills all the grass that is within 3 feet of any point that is 5 feet away from $O$ - i.e. all the grass at points $P$ with $2 \leq O P \leq 8$. The area of this annulus is then $\pi\left(8^{2}-2^{2}\right)=60 \pi$ square feet.