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Calculate the area of shaded portion where AB, BC, CD and AD are quadrants of circle with radius 7 cm. (Use $π = 227$ )

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c m 2

c m 2

c m 2

c m 2

answer is D.

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Detailed Solution

Given that the radius of the circle is 7 cm.
We have to find the area of the shaded region.
The expression to find the area of a quadrant is

A = π r 2 4

, where r is the radius of a circle.
The side of the square is 14cm.
Area of the square,

A 1

is,

A 1 = 142 ∴ A 1 = 196 c m 2

Area of the quadrants,

A 2

is,

A 2 = 4 × π r 2 4 ⇒ A 2 = 4 × 22 × 7 × 7 7 × 4 ⇒ A 2 = 38.5 c m 2

Then, the area of the shaded part,

A s

is,

A s = A 1 − 4 A 2 ⇒ A s = 14 × 14 − 4 14 π r 2 ⇒ A s = 196 − 4 14 π 72 ⇒ A s = 42 cm 2

The area of the shaded portion is 42

c m 2

.
Therefore, the correct option is 4.

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