Question

Dan Perkins goat is attached to the corner of the 8-foot-by-4-foot pump house by QN 8-foot length of rope. The goat eats the grass around the pump house. The pattern consists of three-fourths of a circle of radius 8 feet and one-fourth of of a circle of the radius 4feet. What area of the grass can Dan Perkins's goat eat?

Answer 1

The goat is tied in the four corners of an 8-foot by 4-foot pump house. The rope is 8 feet. The goat is eating the grass, forming a circle The pattern is 3/4 of a circle radius 8 and 1/4 of a circle radius 4.

Getting the area of radius of 8 feet
Area = pi * r^2
Area = pi * 8^2
Area = 201.06 feet^2

Getting the area of radius of 4 feet
Area = pi * r^2
Area = pi * 4^2
Area = 50.27 feet^2

3/4 of 201.06 = 150.80 feet ^2
1/4 of 50.27 = 12.60 feet^2

So the total area is 153.40 feet^2