Chapter 12.3, Problem 86E

Grazing goat problems Consider the following sequence of problems related to grazing goats tied to a rope. (See the Guided Project Grazing goat problems.)

60. A circular concrete slab of unit radius is surrounded by grass. A goat is tied to the edge of the slab with a rope of length 0 ≤ a ≤ 2 (see figure). What is the area of the grassy region that the goat can graze? Note that the rope can extend over the concrete slab. Check your answer with the special cases a = 0 and a = 2.