A dog is leashed to the corner of a house with a 15 foot leash. How much running area does the dog have? Round your answer to the nearest square foot.

If the dog were on a 15-ft leash tied to a stake in the ground

out in the middle of a field, then he could cover every blade

of grass in a 15-ft circle. The area of a circle is (pi R²), so

he would have free range over (pi · 15²) square feet of area.

Sadly, he's not out in the middle of a field. He's tied to the corner

of the house. So he can't cover the whole circle, because the house

blocks a quarter of the circle. The dog only has access to

(3/4) of (pi R²)

= (0.75) · π · (15²)

= (0.75 · π · 225) = 530 square feet (rounded)

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