Name: Area of Combined Figures
Uploaded: 2019-07-19
Duration: 5 min 1 s
Description: We come across various plane figures that are a combination of two or more plane figures such as window designs or circular paths. Let's learn about the area...

Question

$A B$ and $C D$ are respectively arcs of two concentric circles of radii $21 c m$ and $7 c m$ and centre $O$ as shown in the figure. If $∠ A O B = 30 °,$ find the area of the shaded region.

Accepted Answer

Given radius of larger circle $C D$ and radius of smaller circle $= 7 cm$

$Area of sector of angle θ = \frac{θ}{360^{o}} \times {πr}^{2}$

Area of shaded region $=$ area of sector $O A E B -$ area of sector $O C F D$
$= \frac{30^{o}}{360^{o}} \times π \times {(21)}^{2} - \frac{30^{o}}{360^{o}} \times π \times {(7)}^{2}$

$= \frac{1}{12} \times π [{(21)}^{2} - {(7)}^{2}]$
$= \frac{1}{12} \times \frac{22}{7} \times [(21 - 7) (21 + 7)]$
$= \frac{22 \times 14 \times 28}{12 \times 7}$
$= \frac{308}{3} c m^{2}$
$= 102.6 c m^{2}$
Therefore, area of shaded region $= 102.6 c m^{2}$

$A B$ and $C D$ are respectively arcs of two concentric circles of radii $21 c m$ and $7 c m$ and centre $O$ as shown in the figure. If $∠ A O B = 30 °,$ find the area of the shaded region.

Important Questions on Areas Related to Circles

Learn and Prepare for any exam you want !

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O as shown in the figure. If ∠AOB=30°, find the area of the shaded region. ​​​​​​​

Important Questions on Areas Related to Circles

Learn and Prepare for any exam you want !

$A B$ and $C D$ are respectively arcs of two concentric circles of radii $21 c m$ and $7 c m$ and centre $O$ as shown in the figure. If $∠ A O B = 30 °,$ find the area of the shaded region.