Problem: A circular grass plot feet in diameter is cut by a straight gravel path feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grass area is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let denote the center of the plot (See figure) and the midpoint of the other side of the walk. If denotes one arc cut off by the waik, then one half the area of the walk consists of a sector and a right . Denoting areas by parentheses,
(Required Area) ( Plox )(Walk)
(Sectors )
=36 \pi-2 \times \frac{1}{2} \times \frac{\pi}{6} \times 6 \times 6-2 \times \frac{1}{2} \times 3 \times 3 \sqrt
or choice (E).
