Question

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

Answer 1

Circumference of the circle = $2\mathrm{\pi r}$
$$\begin{gathered} \Rightarrow 22=2\times \frac{22}{7}\times \mathrm{r} \\ \Rightarrow \mathrm{r}=\frac{22\times 7}{2\times 22} \\ \Rightarrow \mathrm{r}=3.5\mathrm{cm} \end{gathered}$$
Area of the circle = ${\mathrm{\pi r}}^2$
$$\begin{gathered} =\frac{22}{7}\times 3.5\times 3.5 \\ =38.5{\mathrm{cm}}^2 \end{gathered}$$

Area of the quadrant = $\frac{38.5}{4}=9.625{\mathrm{cm}}^2$