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What will be the area of the shaded region, if in the given figure, O is the centre of the bigger circle, and AC is its diameter, with another circle with AB as diameter drawn having AC=54 cm and BC=10 cm?

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775 cm 2

774 cm 2

770 cm 2

778 cm 2

answer is C.

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Detailed Solution

We have to find the area of the shaded region, if in the given figure, O is the centre of the bigger circle, and AC is its diameter, with another circle with AB as diameter drawn having AC=54 cm and BC=10 cm.
Question Image

Note that, OA and OC are equal to 27 cm,

∴ A B = A C − B C = 54 − 10 = 44 cm

Note that, AB is the diameter of the smaller circle.
So, the radius of the smaller circle:

= A B 2 = 442 = 22 cm

Calculating the area of the smaller circle,
Using the formula,
Area of a circle

= π r 2

, where r is the radius.

∴ Area of the smaller circle = 227 × 22 × 22 = 1521.14 cm 2

Therefore, radius of the larger circle = A C 2 = 542 = 27 cm

Calculating the area of the larger circle,

Area of the larger circle = 227 × 27 × 27 = 2291.14 cm 2

Calculating the area of the shaded region,
= 1521.14-2291.14
=770 square cm
So, the area of the shaded region is

770 cm 2

.
Therefore, option 3 is correct.

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