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Find the area of the shaded region in figure, if ABCD is a rectangle with sides $8 cm$ and $6 cm$ and $O$ is the centre of circle. (Take $π = 3.14)$

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60 cm

30 cm

30.5 cm

42 cm

answer is A.

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Detailed Solution

Given that, ABCD is a rectangle with sides

8 cm

and

6 cm

and

O

is the centre of circle.
Question Image

Determine the area of the rectangle A

1

by using the formula

A 1 =

length \times breadth

\Rightarrow

A 1 = 6 × 8

= 48
The length of the diagonal of rectangle will represent the diameter of the circle.
The diagonal is making a right hand triangle in which hypotenuse is missing so use Pythagorean theorem,

H 2 = B 2 + P 2

Determining the length of the diagonal.

A C 2 = A B 2 + B C 2

\Rightarrow

A C 2 = 64 + 36

\Rightarrow

A C 2 = 100

\Rightarrow

AC = 10
The diameter of the circle is 10 cm so determine its radius r.

r = 102

\Rightarrow r

= 5
Determine the area of the circle by using the formula,

A 2 = π r 2

\Rightarrow

A 2 = p 52

\Rightarrow A_{2}

= 25 3.14

\Rightarrow A_{2}

= 78.5
Determine the area related to the shaded region S by subtracting the area of rectangle

A 1

from the area of circle

A 2

S = A 2 − A 1

\Rightarrow S

= 78.5 − 48

\Rightarrow S

= 30.5
Thus, the area represents the shaded region is 30.5 cm.
Hence the correct option is 1.

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