Question

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 Fig. 11.8). 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)

Answer 1

From the figure, it can be observed that the horse can graze a sector of 90° in a circle of 5 m radius. 

(i) Area that can be grazed by horse = Area of sector OACB = \(\frac{90°}{ 360°} \pi r^2\)
= \(\frac{1}4 \times 3.14 \times (5)^2\)
= 19.625 m\(^2\)

Area that can be grazed by the horse when length of rope is 10 m long = \(\frac{90°}{360°} \times \pi \times ( 10)^2\)
= \(\frac{1}4 \times 3.14 \times 100\)
= 78.5 m\(^2\)

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(ii) Increase in grazing area = (78.5 − 19.625) m\(^2\) = 58.875 m\(^2\)