Question -
Answer -
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)
Solution:
As the horse is tied at one end of a squarefield, it will graze only a quarter (i.e. sector with θ = 90°) of the fieldwith radius 5 m.
Here, the length of rope will be the radius ofthe 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 wherethe horse can graze = ¼ (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 wherethe horse can graze = ¼ (the area of the circle)
= 314/4 = 78.5 m2
∴ Increase in the grazing area = 78.5 m2 – 19.625m2 = 58.875 m2