A horse is tied to a pole fixed at one corner of a 30 m Ă 30 m square field ofgrass, by means of a 10 m long rope (figure).
[Take Ď = 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
â 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
â Increase in the area of the field in which the horse can graze = (314 - 78.5) m 2
= 235.5 m 2