Physics

# Three coins of the same size (radius $1cm$) are placed on table such that each of them touches the other two. The area enclosed by the coins is:

##### ANSWER

$\left( \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$

##### SOLUTION
Radius of each coin $=1\ cm$
With all the three centres an equilateral triangle of side 2 cm is formed.
Area enclosed by coind $=$ Area of equilateral triangle $-3\times$ Area of sector of angle $60^{o}$
$=\dfrac{\sqrt3}{2}(2)^2-3\times\dfrac{60}{360}\times\pi(1)^2$
$=\dfrac{\sqrt3}{4}\times4-3\times\dfrac{1}{6}\times\pi$
$=\left(\sqrt3-\dfrac{\pi}{2}\right)\ cm^2$

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Single Correct Medium Published on 18th 08, 2020
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