Question

Thee length of a side of a square field is 200 mtr. A cow is tired at the corner by means of a 7 mtr long rope . find the area of the field which cow can graze. If the length of rope is doubled then find the increase in the grazing area.

Answer 1

Length of a side of a square field $=20m$

Area of square field $=20m\times 20m=400m^2$

As the cow is tired at the corner by means of a $7m(=r)$ long rope.

The cow can graze a quarter circle of radius $7m$.

Area the cow can graze $A=\frac{\pi \times r\times r}{4}=\frac{\pi \times 7\times 7}{4}=38.48m^2$

As the length of the rope is doubled, r is doubled, $A^{\prime }=\frac{\pi \times 2r\times 2r}{4}=\frac{4\times \pi \times r\times r}{4}=4A$

The increase in grazing is $4A-A=3A=3\times 38.48=115.44m^2$