A horse is tied to a peg at one corner of a square shaped grass field of side $\displaystyle 15$ m by means of a $\displaystyle 5$ m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in grazing area if length of rope is increased to $\displaystyle 10$ m . (Use $\displaystyle \pi=3 \cdot 14$ )

Area of that part of the field in which the horse can graze by means of a $\displaystyle 5$ m long rope \(\displaystyle =\frac{1}{4} \times 3.14 \times(5)^{2}\) \[=19.625 m^{2} \] Area of that part of the field in which the horse can graze by means of a $\displaystyle 10$ m long rope \(\displaystyle \boldsymbol{=} \frac{\mathbf{1}}{\mathbf{4}} \boldsymbol{\times} \mathbf{3 . 1 4} \boldsymbol{\times} \boldsymbol{(} \mathbf{1 0} \boldsymbol{)}^{\mathbf{2}}\) \[=78.5 \mathrm{~m}^{2} \] Increase in grazing area \(\displaystyle =78.5 m^{2}-19.625 m^{2}=58.875 m^{2}\)