Running in Circles

Peanut, the overexcited dog, has lots of energy and is tearing apart the house. Peanut’s owner decides to tie Peanut up in the backyard. He puts a stake in the middle of the yard and attaches one end of a rope to the stake and the other end to Peanut’s collar.

Still full of energy, Peanut runs in circles, stretching the rope as far as he can from the stake. He makes 40 laps around the stake and travels a total distance of 1 mile. All this running has left Peanut tired and thirsty. If his bowl of water is 20 feet away from the stake, can he get a drink? Explain your answer. (Assume the rope is tied around the stake with a loop so that it will not wrap around the stake.)

(Source: The Math Forum)

What area does Peanut have to play in outside, when he is tied to his stake?