In the given figure, are shown sectors of two concentric circles of radii 7 cm and 3.5 cm. Find the area of the shaded region. (Use π=22/7)

Question

In the given figure, are shown sectors of two concentric circles of radii 7 cm and 3.5 cm. Find the area of the shaded region. \(\big(Use\,π = \frac{22}{7}\big)\) 

Answer 1

Required area = Area of sector OAB – Area of sector OCD

\(\big(\frac{30}{360} \times \frac{22}{7} \times 7^2\big) \;{cm}^2\) - \(\big(\frac{30}{360} \times \frac{22}{7} \times 3.5^2\big) \;{cm}^2\)

= \(\frac{77}{6}\) cm² - \(\frac{77}{24}\) cm² = \(\frac{77}{24}\) × (4 - 1) = \(\frac{77}{8}\) cm² 

= 9.625 cm².