Question

Find the area of a quadrant of a circle whose circumference is 44 cm. [CBSE 2011]

Answer 1

Let the radius of the circle be r.
​Now,
$$\begin{gathered} \mathrm{Circumference}=44 \\ \Rightarrow 2\mathrm{\pi }r=44 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$
Now,
Area of quadrant = $\frac{1}{4}\mathrm{\pi }{r}^2=\frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2=38.5{\mathrm{cm}}^2$
Hence, the area of the quadrant of the circle is 38.5 cm².