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 π = 3.14)
Here, the length of rope will be the radius of the circle i.e. r = 5 m
It is also known that the side of square field = 15 m
(i) Area of circle = πr2 = 22/7 × 52
= 78.5 m2
Now, the area of the part of the field where the horse can graze = 1/4 (the area of the circle) = 78.5/4 = 19.625 m2
(ii) If the rope is increased to 10 m,
Area of circle will be = πr2 = 22/7×102
= 314 m2
Now, the area of the part of the field where the horse can graze = 1/4 (the area of the circle)
= 314/4 = 78.5 m2
∴ Increase in the grazing area = 78.5 m2 – 19.625 m2
= 58.875 m2