Question

Find the area of the shaded region in figure, where radii of the two concentric circles with centre O are $7$cm and $14$cm respectively and $\angle AOC={40}^o$.

• A. $410.67c{m}^2$
• B. $40.67c{m}^2$
• C. $10.67c{m}^2$
• D. None of these

Answer 1

Answer: (A)

$410.67c{m}^2$

We have,
Area of ring $=\pi (R^2-r^2)$
$=\pi \times ({14}^2-7^2)$
$=462c{m}^2$
Area of the region ABDC
=Area of sector AOC-Area of sector BOD
$=\left(\frac{40}{360}\times \frac{22}{7}\times 14\times 14-\frac{40}{360}\times \frac{22}{7}\times 7\times 7\right)c{m}^2$
$=\left(\frac{1}{9}\times 22\times 14\times 2\frac{1}{9}\times 22\times 7\times 1\right)c{m}^2$
$=\frac{22}{9}\times (28-7)c{m}^2=\frac{154}{3}c{m}^2$
Hence, Required shaded area
$=(462-\frac{154}{3})c{m}^2$
$=\frac{1232}{3}c{m}^2=410.67c{m}^2$