Question

A horse is tied to a pole fixed at one corner of a $30m\times 30m$ square field of grass, by means of a $10m$ long rope. Find the area of the field, in which the horse can graze? (Take $\pi =3.14$)

• A. $78.5sq.m$
• B. $79.5sq.m$
• C. $76.0sq.m$
• D. $78.0sq.m$

Answer 1

The correct option is A $78.5sq.m$

Side of a square $=30m$

Length of the rope $=$ Radius of the sector

$\therefore$ Radius of the sector $r=10m$

Measure of arc $\theta ={90}^o$ [Angle of a square]

Area of field that can be grazed $=$ Area of sector

$=\frac{\theta }{360}\times \pi r^2$

$=\frac{90}{360}\times 3.14\times 10\times 10$

$=\frac{1}{4}\times 314$

$=78.5m^2$