Question

AS RELATED TO CIRCLES
117
Find the area of the shaded region in Fig. 5.20. if radii of the two concentric circles with
centre o are 7 cm and 14 cm respectively and Z AOC = 40°.
Fig. 5.21
Fig. 5.20​

Answer 1

Solution:

Note: Diagram pf this question attached on attachment file.

Given:

=> Radius of outer part = 14 cm.

=> Radius of inner part = 7 cm.

=> Ф = 40°

To find:

=> Shaded region

Formula used:

$\sf{\implies Area\;of\;sector = \dfrac{\theta}{360^{\circ}}\pi r^{2}}$

So,

$\sf{Area\;of\;sector(AOC)=\dfrac{\theta}{360^{\circ}}\pi r^{2}}$

$\sf{\implies \dfrac{40}{360}\times \dfrac{22}{7}\times 14\times 14}$

$\sf{\implies \dfrac{1}{9} \times 22\times 2\times 14}$

$\sf{\implies \dfrac{616}{9}\;cm^{2}}$

Now,

$\sf{Area\;of\;sector(BOD)=\dfrac{\theta}{360^{\circ}}\pi r^{2}}$

$\sf{\implies \dfrac{40}{360} \times \dfrac{22}{7}\times 7\times 7}$

$\sf{\implies \dfrac{1}{9} \times 22\times 7}$

$\sf{\implies \dfrac{154}{9}\;cm^{2}}$

Now, area of the shaded region = [Area of sector AOC] - [Area of sector BOD]

$\sf{\implies \dfrac{616}{9}-\dfrac{154}{9}}$

$\sf{\implies \dfrac{1}{9}[616-154]}$

$\sf{\implies \dfrac{1}{9}\times 462}$

${\boxed{\boxed{\sf{\implies \dfrac{154}{3}\;cm^{2}}}}}$