Question

A horse is placed for grazing inside a rectangular field $70m$ by $52$m and is tethered to one corner by a rope $21$m long. On how much area can it graze?

• A. $346.5c{m}^2$
• B. $360c{m}^2$
• C. $350.5c{m}^2$
• D. $380c{m}^2$

Answer 1

The correct option is A $346.5c{m}^2$

Shaded portion indicates the area which the horse can graze. Clearly, shaded area is the area of a quadrant of a circle of radius $r=21m$.
$\therefore$ Required area $=\frac{1}{4}\pi r^2$
$\therefore$ Required area$=\frac{1}{4}\times \frac{22}{7}\times {21}^2$
$\therefore$ Required area$=\frac{693}{2}c{m}^2=346.5c{m}^2$