Find the area of a flat circular ring formed by two concentric circles (circles with the same centre) whose radii are 9 cm and 5 cm.

Given:

The external radius or the radius of the bigger circle, R = 9 cm

Internal radius or the radius of the smaller circle, r = 5 cm

We know that the area of a circle is ${\mathbf{\pi r}}^{\mathbf{2}}$.

Now, the area of the ring between the two concentric circles:

= Area of the bigger circle - Area of the smaller circle

= ${\mathrm{\pi R}}^2 - {\mathrm{\pi r}}^2$

= $\mathrm{\pi }({\mathrm{R}}^2 - {\mathrm{\pi r}}^2)$

Substituting the values

= $\frac{22}{7}\times (9^2 - 5^2)$ 

= $\frac{22}{7}\times (81 - 25)$

= $\frac{22}{7}\times 56$ 

= $\mathbf{176}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}$

Hence, the required area is $\mathbf{176}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}$.