Question

In the given figure, the sectors of two concentric circles of radii 7 cm and 3.5 cm are shown. Find the area of the shaded region.

Answer 1

Area of the shaded region = (Area of the sector with $r=7\mathrm{cm}\mathrm{and}\theta =30°$) $-$ (Area of the sector with $r=3.5\mathrm{cm}\mathrm{and}\theta =30°$)
$$\begin{gathered} =\left|\left(\frac{22}{7}\times 7\times 7\times \frac{30}{360}\right)-\left(\frac{22}{7}\times 3.5\times 3.5\times \frac{30}{360}\right)\right|{\mathrm{cm}}^2 \\ =\left(\frac{77}{6}-\frac{77}{24}\right){\mathrm{cm}}^2 \\ =\frac{77}{8}{\mathrm{cm}}^2 \\ =9.625{\mathrm{cm}}^2 \end{gathered}$$