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. 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)

(i) From figure,

It is the quadrant of radius 5 m in which horse can graze.

We know that,

Area of quadrant = $\dfrac{1}{4} \times$ Area of circle

Substituting value we get :

$\text{Area of quadrant} = \dfrac{1}{4} \times πr^2 \\[1em] = \dfrac{1}{4} \times 3.14 \times 5^2 \\[1em] = \dfrac{1}{4} \times 3.14 \times 25 \\[1em] = 19.625 \text{ m}^2.$

Hence, area of field in which horse can graze = 19.625 m².

(ii) If rope would be 10 m long, then gazing area of horse would be a quadrant of 10 m.

$\text{Area } = \dfrac{1}{4} \times 3.14 \times 10^2 \\[1em] = \dfrac{1}{4} \times 3.14 \times 100 \\[1em] = \dfrac{314}{4} = 78.5 \text{ m}^2.$

Increase in grazing area = 78.5 - 19.625 = 58.875 m².

Hence, increase in grazing area = 58.875 m².