A horse is tied to a pole fixed at one corner of a 30 m × 30 m square field ofgrass, by means of a 10 m long rope (figure).
[Take π = 3.14.]
(i) Find the area of that part of the field in which the horse can graze.
(ii) Find the increase in the grazing area if the rope were 20 m long insteadof being 10 m long.

(i)

The area of the field in which the horse can graze is one-fourth of a circle made by the rope. [The area in yellow]
Radius of the portion of the circle, r = length of the rope = 10 m
Since,

Area of the field in which the horse can graze = area of Quarter Circle

⇒ Area of the field in which the horse can graze is 78.5 m ² .
(ii)

The radius of the circular portion = length of new rope = 20 m

Area of the field in which the horse can graze = area of Quarter Circle

⇒ Increase in the area of the field in which the horse can graze = (314 - 78.5) m ²
= 235.5 m ²