Question

Find the area of a sector of a circle of radius $28cm$ and central angle $45°$.

Answer 1

Find the area of sector of a circle

Angle subtended at center is $45°=\frac{\mathrm{\pi }}{4}$

Total angle of a circle is $2\mathrm{\pi }$

Therefore the subtended angle is $\frac{\mathrm{\pi }}{4}·\frac{1}{2\mathrm{\pi }}=\frac{1}{8}$ part of the circle.

The radius of the circle is $28cm$.

Therefore the area of the circle is

$$\begin{gathered} ={\mathrm{\pi r}}^2 \\ =\frac{22}{7}·{28}^2 \\ =2464\mathit{}\mathit{}c{m}^2 \end{gathered}$$

Therefore the area of ${\frac{1}{8}}^{th}$ part of the circle is

$$\begin{gathered} =\frac{2464}{8} \\ =308c{m}^2 \end{gathered}$$

Hence, the required area of the sector of a circle is $308c{m}^2$