The diameter of a coin is 1 cm. If four such coins are placed on a table so that each coin touches the other two coins as shown in the figure.

( $π = 3.14$ )

Then the area of shaded region

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0.312

c m 2

0.215

c m 2

0.213

c m 2

0.325

c m 2

answer is B.

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Detailed Solution

We are given that the diameter of circle as
⇒d = 1 cm
We know that the radius of a circle is half of the diameter.
Let us assume that the radius of each circle as ′r′ then we get

⇒ r = d 2 ⇒ r = 12 c m

Let us assume that the side length of square ABCD as ′a′
Here, we can see that the square is formula by adding the radii of two adjacent circles because we are given that each circle touches the remaining two.
We also know that all the circles are identical then we get the side length of square as

⇒ r = 2 r ⇒ a = 2 × 12 ⇒ a = 1 c m

Now, let us assume that the area of square as

A 1

We know that the formula of area of square having side length as ′a′ is given as

⇒ A = a 2

By using this formula we get the area of square as

⇒ A 1 = (1 c m) 2 ⇒ A 1 = 1 c m 2

Now, let us assume that the area of one quarter circle as

A 2

We know that the formula of area of quarter circle having the radius as ′r′ is given as

⇒ A = π r 2 4

By using this formula we get the area of one quarter circle as

⇒ A 2 = π 122 4 ⇒ A 2 = π 16

Now, let us assume that the area of shaded region as A
We know that from the figure that the area of the shaded region is given by removing the areas of four quarter circles from the area of the square.
By converting the above statement into mathematical equation we get