Question

The circumference of a circle is 22 cm. Find the area of its quadrant. [CBSE 2012]

Answer 1

Let the radius of the circle be r.
​Now,
$$\begin{gathered} \mathrm{Circumference}=22 \\ \Rightarrow 2\mathrm{\pi }r=22 \\ \Rightarrow r=\frac{22\times 7}{44}=\frac{7}{2}\mathrm{cm} \end{gathered}$$
Now, Area of quadrant = $\frac{1}{4}\mathrm{\pi }{r}^2=\frac{1}{4}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2=\frac{77}{8}{\mathrm{cm}}^2$
Hence, the area of the quadrant of the circle is $\frac{77}{8}$ cm².