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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.
AC = 54 cm
BC = 10 cm
⇒ AB = AC-BC = 54-10 = 44 cm
Radius of bigger circle = = = 27 cm = r1
Radius of Smaller circle = = = 22 cm = r2
∵ Area of Circle = πr2
∴ Area of Bigger Circle = πr12
= × 27 × 27
Similarly, Area of Smaller Circle = πr22
= × 22 × 22
Area of shaded region = Area of Bigger Circle – Area of Smaller Circle = - = = 770 cm2
Hence, Area of Shaded Region is 770 cm2.