Four equal circles, each of radius $ 5 \mathrm{~cm} $, touch each other as shown in the below figure. Find the area included between them (Take $ \pi=3.14 $ ).
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Given:

Four equal circles, each of radius \( 5 \mathrm{~cm} \), touch each other as shown in the figure.

To do: 

We have to find the area included between them.

Solution:

Radius of each circle $= 5\ cm$.

The four circles touch each other externally

This implies, we get a square by joining the centres of the circles.

Length of each side of the square $=5 + 5 = 10\ cm$

Area of the square $= (10)^2$

$= 100\ cm^2$

Area of four quadrants inside the square $= 4 \times \frac{1}{4} \pi r^2$

$= \pi r^2$

$= 3.14 \times 5^2\ cm^2$

$= 3.14 \times 25\ cm^2$

$= 78.5\ cm^2$

Therefore,

Area of the part included between the circles $=$ Area of the square $-$ Area of the four quadrants

$= 100 - 78.5$

$= 21.5\ cm^2$

The area included between the circles is $21.5\ cm^2$.

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Updated on: 10-Oct-2022

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