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.

Given:

AC = 54 cm

BC = 10 cm

⇒ AB = AC-BC = 54-10 = 44 cm

Radius of bigger circle = = = 27 cm = r_{1}

Radius of Smaller circle = = = 22 cm = r_{2}

∵ Area of Circle = πr^{2}

∴ Area of Bigger Circle = πr_{1}^{2}

= × 27 × 27

= cm^{2}

Similarly, Area of Smaller Circle = πr_{2}^{2}

= × 22 × 22

= cm^{2}

Area of shaded region = Area of Bigger Circle – Area of Smaller Circle = - = = 770 cm^{2}

__Hence, Area of Shaded Region is 770 cm ^{2}.__

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