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 `("Take"  π = 22/7)`.

Answer 1

Given: Two circles with centres A and B touch at C. AC = 8 cm, AB = 3 cm. `("Take"  π = 22/7)`.

Step-wise calculation:

1. Radius of larger circle R = AC = 8 cm.

2. Distance between centres AB = 3 cm.

So, radius of smaller circle

r = R – AB

= 8 – 3

= 5 cm

3. Shaded area

= Area of larger circle – Area of smaller circle 

= π(R² – r²) 

= `22/7 (8^2 - 5^2)`

= `22/7 (64 - 25)`

= `22/7 xx 39` 

= `858/7` cm²

= `122 4/7` cm² 

= 122.5714286 cm²

Area of the shaded region

= `858/7` cm² 

= `122 4/7` cm² 

= 122.57 cm²