Question

A horse is placed for grazing inside a rectangular field 40 m by 36 m and is tethered to one corner by a rope 14 m long. Over how much area can it graze? (Take π = 22/7)

Answer 1

It is given that a horse is tethered to one corner of a rectangular field (40 m × 36 m) by a 14 m long rope.

Let r m be the radius of a circle. Then area A of circle is

$$\begin{gathered} A={\mathrm{\pi r}}^2{\mathrm{m}}^2 \\ =\frac{22}{7}\times 14\times 14{\mathrm{m}}^2 \\ =616{\mathrm{m}}^2 \end{gathered}$$

Since the horse can graze inside the rectangular field only, the required area is quadrant of circle. So,

$\mathrm{Required}\mathrm{area}=\frac{\mathrm{A}}{4}=\frac{616}{4}=154{\mathrm{m}}^2$

Hence the horse can graze 154 m² area.