Question

A cow is tied to a pole fixed at one corner of a 20 m $\times$ 20 m square agricultural field by a 10 m long rope. Find the area of that part of the field in which the cow cannot graze. (Take $\pi =3.14$)

• A. 221.5 $m^2$
• B. 350 $m^2$
• C. 321.5 $m^2$
• D. 400 $m^2$

Answer 1

The correct option is C 321.5 $m^2$

Area of the field in which cow cannot graze = Area of square - Area of agricultural field in which the cow can graze

Area of Square = 20$\times$20 = 400 $m^2$

The area of agricultural field in which the cow can graze is the area of sector with radius 10 m and angle made by it at the centre is ${90}^{\circ }$

Area of sector = $\frac{x^{\circ }}{{360}^{\circ }}\pi r^2$

$\therefore$ Area of agricultural field in which the cow can graze = $\frac{{90}^{\circ }}{{360}^{\circ }}$$\times$3.14$\times$ ${10}^2$

= 78.5 $m^2$

Hence,
Area of the field in which cow cannot graze = 400 - 78.5 = 321.5 $m^2$