As the cow moves around the shed, the rope tethering the cow will WRAP AROUND the shed, as shown in the figure above.
As the cow moves COUNTERCLOCKWISE, the 5-unit rope will wrap 4 UNITS TO THE LEFT (along the top of the shed) and 1 UNIT DOWN (along the left side of the shed).
As the cow moves CLOCKWISE, the 5-unit rope will wrap 3 UNITS DOWN (along the right side of the shed) and 2 UNITS TO THE LEFT (along the base of the shed).
The result is that the cow can access the 3 shaded regions.
Blue region:
This region is equal to 3/4 of a circle with a center at A and a radius of 5.
Area = (3/4)(π)(5²) = (75/4)π.
Yellow region:
This region is equal to 1/4 of a circle with a center at B and a radius of 2.
Area = (1/4)(π)(2²) = π.
Red region:
This region is equal to 1/4 of a circle with a center at C and a radius of 1.
Area = (1/4)(π)(1²) = (1/4)π.
Total accessible area = blue region + red region + yellow region = (75/4)π + (1/4)π + π = (76/4)π + π = 20π.
The correct answer is
E.
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