Question

A cow is tied with a rope of length $14m$ at the corner of a rectangular field of dimensions $20m\times 16m$. The area of the field in which the cow can graze is :

• A. $77m^2$
• B. $140m^2$
• C. $90m^2$
• D. $154m^2$

Answer 1

The correct option is D $154m^2$

Given-ABCD is a rectangular field of dimensions $20m\times 16m.$

A cow tied by a rope $BP=BQ=14m$ at B, is grazing.

Here the cow grazes an area $A$ = Area of Sector with central angle ${90}^o$ and radius $14m.$

$\therefore A=\frac{\theta }{{360}^o}\times \pi \times r^2$ where $\theta =$ Central Angle $={90}^o$,

and

$r=$ radius of the sector$=14m.$

$\therefore A=\frac{{90}^o}{{360}^o}\times \frac{22}{7}\times {14}^2=154m^2.$