Question

Find the area of a quadrant of a circle whose circumference is $22cm$.

Answer 1

$Circumferenceofacircle,$ $2\pi r=22cm$.
$Areaofaquadrantofacircle=?$
$2\pi r=22$
$2\times \frac{22}{7}\times r=22$
$r=22\times \frac{7}{22}\times \frac{1}{2}$
$r=\frac{7}{2}cm$
$\therefore$ $Areaofaquadrantofacircle(\theta ={90}^o)$

$=\frac{90}{360}\times \pi r^2$
$=\frac{1}{4}\times \pi r^2$
$=\frac{1}{4}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2$
$=\frac{1}{4}\times \frac{22}{7}\times \frac{49}{4}$
$=\frac{77}{8}$
$=9.62sq.cm$.