In fig., sectors of two concentric circles of radii 7 𝑐𝑚 and 3. 5 𝑐𝑚 are given. Find the area of the shaded region. (Use π = 22/7 )

We are given the radii of the two concentric sectors, and we have to find the area of the shaded region.

The area of the shaded region can be found by subtracting the area of the smaller sector from the area of the bigger sector.

Now, we know that area of a sector is given by 𝐴 = $\frac{\theta }{360°}\times {\mathrm{\pi r}}^2$ , where θ is the sector's

angle is enclosed, and 𝑟 is the radius of the sector. The radius of the bigger sector, 𝑅 = 7 𝑐𝑚

The radius of the smaller sector, 𝑟 = 3. 5 𝑐𝑚

Both these sectors enclose an angle of 30$°$, i.e.,   θ = 30$°$

Area of bigger circle = $\frac{\theta }{360°}\times \pi R^2$

𝐴 =  $$\begin{gathered} \frac{30°}{360°}\times \frac{22}{7}\times 7\times 7 \\ \frac{1}{12}\times 22\times 7 \\ \frac{154}{12} \end{gathered}$$

A = 12.83 cm²

Area of Smaller circle = $\frac{\theta }{360°}\times \pi r^2$

a= $$\begin{gathered} \frac{30°}{360°}\times \frac{22}{7}\times 3.5\times 3.5 \\ \frac{1}{12}\times 22\times 3.5\times 0.5 \\ \frac{38.5}{12} \\ 3.21 c{m}^2 \end{gathered}$$

So, the area of the shaded region = 𝐴 − 𝑎
= 12. 83 − 3. 21
= 9. 62 𝑐𝑚²
Hence, the area of the shaded region is 9.62 cm²