Question

What is the area of a quadrant of a circle whose circumference is 22 cm?
$(\pi =\frac{22}{7})$

• A. $\frac{77}{8}c{m}^2$
  
• B. $\frac{77}{16}c{m}^2$
  
• C. $\frac{49}{16}c{m}^2$
  
• D. $\frac{49}{8}c{m}^2$
  

Answer 1

The correct option is A $\frac{77}{8}c{m}^2$


Quadrant of a circle is a sector measuring an angle of ${90}^{\circ }$ at the centre of the cirle.

Circumference of the circle is given by
$=2\pi r=22cm$
$Hence,radius\left(r\right)=\frac{22}{2\pi }cm=\frac{7}{2}cm$

Area of the sector making angle $\theta$
$=\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi r^2$

Area of the sector making angle ${90}^{\circ }$
$=\left(\frac{{90}^{\circ }}{{360}^{\circ }}\right)\times \pi r^{2}c{m}^2$
$=\left(\frac{1}{4}\right)\times (\frac{7}{2}{)}^2\pi =(\frac{49}{16})\pi c{m}^2=\frac{77}{8}c{m}^2$