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
$=1662.57-452.57$
$=1210 \mathrm{~cm}^{2}$
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