Question

A horse is tied to a peg at one corner of a square shaped grass field of side $15m$ by means of a $5m$ long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were $10m$ long instead of $5m$. (Use $\pi =3.14$)

Answer 1

Side of square field $=15m$

Length of rope $=5m=$radius of the quadrant

The area available for the horse to graze = Area of Quadrant of a circle

$\therefore$ Area of Quadrant having radius $5cm$ $=\frac{\pi \times r^2}{4}$

$=\frac{3.14\times 5\times 5}{4}$

$=\frac{78.5}{4}$

$=19.625m^2$
If the length of rope is increased to $10m$, then the new radius $=5+5=10m$
$\therefore$ Area of new quadrant having radius $10cm$ $=\frac{\pi \times r^2}{4}$

$=\frac{3.14\times 10\times 10}{4}$

$=\frac{314}{4}$
$=78.5m^2$
$\therefore$ Increase in grazing area $=$ Area of new quadrant having radius $10cm$ $-$ Area of Quadrant having radius $5cm$

$=78.5-19.625=58.875m^2$