Question

Find the area of the shaded region in Fig. if radii of the two concentric circles with center O are $7cm$ and $14cm$ respectively and $\angle AOC=40°$

Answer 1

Area of a sector$=\frac{1}{2}{r}^2\frac{\theta °}{180}\pi$

A (sector BOD)$=\frac{1}{2}\times 49\times \frac{40}{180}\pi c{m}^2$

$=\frac{49\times 2}{18}c{m}^2$

$=\frac{49}{9}\pi c{m}^2$

A (sector AOC)$=\frac{1}{2}\times 196\times \frac{40}{180}c{m}^2$

$=\frac{196}{9}\pi c{m}^2$

Area of shaded region = A (sector AOC)-A (sector BOD)

$=\frac{196-49}{9}\pi c{m}^2$

$=\frac{147}{9}\pi c{m}^2$

$=\frac{147}{9}\times \frac{22}{7}c{m}^2$

$=51.34c{m}^2$