Question

In the following figure, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.​

Answer 1

Answer:

The area of shaded region is 122.57 cm²

Step-by-step explanation:

Given :  

AC = 8 cm & AB = 3 cm

AC is the radius of the bigger circle & BC is the radius of inner circle.

BC = AC - AB  

BC =  8 - 3  

BC = 5 cm

Radius of inner circle, r = 5 cm

Radius of bigger circle , R = 8 cm

Area of shaded region ,A = Area of bigger circle -  Area of inner circle

A = πR² - πr²

A = π(R² - r²)

A = 22/7 (8² - 5)

A = 22/7 (64 - 25)

A = 22/7 × 39

A = (22×39)/7

A = 858/7  

A = 122.57 cm²

Area of shaded region = 122.57 cm²

Hence, the area of shaded region is 122.57 cm²

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\huge\underline\mathcal\pink {Solution}$

Given :

AB = 3cm

AC = 8 cm

As we know that AC is the radius of the bigger circle and BC is the radius of the smaller circle .

BC = AC - AB

= BC = 8 - 3

= BC = 5 cm

It means the radius of the smaller circle is 5 cm .

=> R = 8 cm

and r = 5 cm

Now ,

Area of shaded region = Area of bigger circle - Area of smaller circle

$= \pi {R}^{2} - \pi {r}^{2}$

$= \pi( {8})^{2} - \pi( {5})^{2}$

$=64\pi - 25\pi$

$= \pi(64 - 25)$

$= 39\pi$

Hence , the area of the shaded region is $39\pi {cm}^{2}$