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 $ ). "
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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