There is a square board of side 2a units circumscribing a circle as shown in the figure. The area of shaded portion in sq. units is

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Solution

Q.
There is a square board of side 2a units circumscribing a circle as shown in the figure. The area of shaded portion in sq. units is:

1 $π / 4 - a^{2}$

2 $(4 - π) a^{2}$

3 $(4 - π) / 4$

4 $4 / π$

Ans.
(2)

We have length of the square board = 2a

⇒ Diameter of circle = 2a

⇒ Radius of circle = a

$∴ A r e a o f s q u a r e = (2 a)^{2} = 4 a^{2}$

$A n d, a r e a o f c i r c l e i n s c r i b e d = π a^{2}$

Area of shaded region = Area of square − Area of circle

$= 4 a^{2} - π a^{2} = (4 - π) a^{2}$

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