# A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see figure). Find (i) The area of that part of the field in which the horse can graze. (ii) The increase in the grazing area if the rope were 10 m long instead of 5 m. (Use $$\pi \ = \ 3.14$$ )

(i) The horse will graze over a quadrant of a circle with centre at the corner A of the field and radius AF = 5 m.

Then the area of the quadrant of this circle

$$= \ \frac{ \pi \ × \ 5^2}{4} \ = \ \frac{3.14 \ × \ 25}{4} \ = \ 19.625$$m2

(ii) In the 2nd case, radius = 10 m.

The area of the quadrant of this circle

$$= \ \frac{ \pi \ × \ 10^2}{4} \ = \ \frac{3.14 \ × \ 100}{4} \ = \ 78.5$$ m2

$$\therefore$$ Increase in the grazing area

$$= \ 78.5 \ - \ 19.625 \ = \ 58.875$$m2