Question

The radii of two concentric circles with centre o are 7cm and 14 cm respectively and angle aoc=40°. Find the shaded region

Answer 1

Figure dekh le bhai sahi h ya nahi

Answer 2

$\frac {154}{3}$ is the required area

Step-by-step explanation:

$r_1$ = 7 cm (For OBDO sector)

$r_2$= 14 cm (For OACO sector)

and $\theta = 40$°

Area of Sector OBDO = $\pi (r_1)^2 \times \frac {\theta}{360}$

= $\frac {22}{7} \times 7 \times 7 \times \frac {40}{360}$

= $\frac {154}{9}\ cm^2$

Area of sector OACO = $pi (r_1)^2 \times \frac {\theta}{360}$

= $\frac {22}{7} \times 14 \times 14 \times \frac {40}{360}$

= $\frac {616}{9}\ cm^2$

Hence,

Area of Shaded region = Area of sector OACO - Area of Sector OBDO

= $\frac {616}{9} - \frac {154}{9}$

= $\frac {616-154}{9}\ cm^2$

= $\frac {462}{9} = \frac {154}{3}\ cm^2$