The diameter of a coin is $ 1 \mathrm{~cm} $. If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take $ \pi=3.1416) $
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Given:

The diameter of a coin is \( 1 \mathrm{~cm} \).

Four such coins be placed on a table so that the rim of each touches that of the other two.

To do: 

We have to find the area of the shaded region.

Solution:

Diameter of each coin $=1\ cm$

This implies,

Radius of each of the coin $r= \frac{1}{2}\ cm$

$=0.5\ cm$

A square is formed by joining the centres of the coins.

This implies,

Diameter of the circle $=$ Length of the side of the square

$=1\ cm$

Therefore,

Area of the shaded region $=$ Area of the square $-$ Area of four quadrants inside the square

$=(1)^{2}-4 \times \frac{1}{4} \pi (0.5)^{2}$

$=1-3.14 \times 0.25$

$=1-0.785$

$=0.215 \mathrm{~cm}^{2}$

The area of the shaded region is $0.215\ cm^2$.

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Updated on: 10-Oct-2022

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