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What will be the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8cm and 6cm and O is the centre of the circle?

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An Intiative by Sri Chaitanya

30.57 cm 2

35.57 cm 2

38.57 cm 2

40.57 cm 2

answer is A.

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Detailed Solution

We have to find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8cm and 6cm and O is the centre of the circle.
Note that,
In the right-angled triangle ABC,
By Pythagoras Theorem,

A C 2 = A B 2 + B C 2 A C 2 = 82 + 62 A C 2 = 64 + 36 A C 2 = 100

∴ A C = 10 cm

So, Radius of the circle:

O A = 12 A C = 5 cm

Calculating the area of the shaded region,
Area of the shaded region = Area of circle − Area of rectangle ABCD

Area of circle = π r 2

Area of rectangle =

l × b

= π (O A) 2 − A B × B C = 227 × (5) 2 − 8 × 6 = 78.57 − 48 = 30.57 cm 2

So, the area of the shaded region is

30.57 cm 2

.
Therefore, option 1 is correct.

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