Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.
Question:

Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.

Solution:

Let r1 cm and r2 cm be the radii of the outer and inner boundaries of the ring, respectively.
We have:

$r_{1}=23 \mathrm{~cm}$

$r_{2}=12 \mathrm{~cm}$

Now,

Area of the outer ring $=\pi r_{1}^{2}$

$=\frac{22}{7} \times 23 \times 23$

$=1662.57 \mathrm{~cm}^{2}$

Area of the inner ring $=\pi r_{2}{ }^{2}$

$=\frac{22}{7} \times 12 \times 12$

$=452.57 \mathrm{~cm}^{2}$

Area of the ring = Area of the outer ring Area of the inner ring

$=1662.57-452.57$

$=1210 \mathrm{~cm}^{2}$