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

Let the radius of the circle be r 

Thus, the Circumference of a circle  = 2$\mathrm{\pi }$r = 22 cm

Therefore, r = Circumference /2$\mathrm{\pi }$

we know that, A quadrant of a circle means one of the four equal parts. 

Therefore, 

the area of a quadrant = $\frac{1}{4}$ $\times$ Area of a circle

= 1/4 $\times$ $\mathrm{\pi }$r²

Radius = r = circumference/2π

= 22/(2 $\times$ 22/7)

= (22 $\times$ 7)/(2 $\times$ 22)

= 7/2 cm

Therefore, the area of a quadrant = $\frac{1}{4}$ × $\mathrm{\pi }$r²

= 1/4 $\times$ 22/7 $\times$ 7/2 $\times$ 7/2

= 77/8 cm²