1973 AHSME Problems/Problem 25
Problem
A circular grass plot 12 feet in diameter is cut by a straight gravel path 3 feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grass area is
Solution
The wanted area can be divided into a semicircle and a circular segment. The area of the semicircle is square feet. To find the area of the circular segment, note that by using 30-60-90 triangles (or Law of Cosines), the chord's length is ft, and the angle of the sector is . That means the area of the circular segment is square feet. Thus, the area of the remaining grassy area is square feet.
See Also
1973 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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