Question

The circumference of a circle is 22 cm. The area of its quadrant (in cm²) is
(a) $\frac{77}{2}$

(b)$\frac{77}{4}$

(c)$\frac{77}{8}$

(d)$\frac{77}{16}$

Answer 1

Let the radius of the circle be r cm.
Now, circumference of circle = 22
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }r=22 \\ \Rightarrow 2\times \frac{22}{7}\times r=22 \\ \Rightarrow r=\frac{7}{2}\mathrm{cm} \end{gathered}$$
Area of quadrant = $\frac{1}{4}\mathrm{\pi }{r}^2=\frac{1}{4}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{8}{\mathrm{cm}}^2$

Hence, the correct answer is option (c).