Question

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

Answer 1

Let the radius of the circle be $r$.
circumference = $22cm$
$2πr$ = $22$
$r$ = $\frac{22}{ 2π}$ = $\frac{11}{ π}$

Quadrant of circle will substend $90^{\degree}$angle at the centre of the circle.

Area of such quadrant of the circle = $\frac{90^{\degree}}{ 360^{\degree} }\times π r^2$

= $\frac{1}{ 4} \times π \times (\frac{11}{π})^2$

= $\frac{121}{ 4π }$= $\frac{121 \times 7 }{ 4 \times 22}$

= $\frac{77}{8} cm^2$

Therefore, area of a quadrant of a circle is $\frac{77}{8} cm^2$.