A goat is tied at one corner of a 12 feet by 16 feet barn. If the rope is 24 feet long, find the area of the region outside the
barn, in which the goats can graze.
1 answer:
Answer:
1520.5 ft²
Step-by-step explanation:
A diagram can be helpful.
The total area is the sum of ...
3/4 of a circle with radius 24 ft
1/4 of a circle with radius 12 ft
1/4 of a circle with radius 8 feet
__
The area of a whole circle is given by ...
A = πr²
so our grazing area is ...
A = (3/4)π(24 ft)² + (1/4)π(12 ft)² + (1/4)π(8 ft)²
= π(432 ft² +36 ft² +16 ft²) = 484π ft²
A ≈ 1520.5 ft²
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