Question

In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find the area of the shaded region.

Answer 1

We have :

OA = OC = 27 cm

AB = AC - BC

= 54 - 10

= 44

AB is the diameter of the smaller circle.

Thus, we have:

Radius of the smaller circle `="AB"/2 = 44/2 =  22  "cm"`

Area of the smaller circle = πr²  

`=22/7xx22xx22`

= 1521.14 cm²

Radius of the larger circle `= "AC"/2 = 54/2 = 27 "cm"`

Area of the larger circle = πr² 

`= 22/7xx27xx27`

= 2291.14 cm² 

∴ Area of the shaded region = Area of the larger circle -- Area of the smaller circle

= 2291.14 - 1521.14

= 770 cm²