Question

The diameter of a coin is $1$ 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 $\pi =3.1416$)

Answer 1

$\Rightarrow$ Diameter of coin $\left(d\right)=1m$

$\therefore$ Radius of coin $\left(r\right)=\frac{1}{2}=0.5m$

$\Rightarrow$ Area of $4$ sectors $=4\times \frac{\theta }{{360}^o}\times \pi r^2$

$\Rightarrow$ Area of $4$ sectors $=4\times \frac{{90}^o}{{360}^o}\times 3.14\times (0.5{)}^2$

$\Rightarrow$ Area of $4$ sectors $=0.785c{m}^2$

$\Rightarrow$ Side of square $=0.5+0.5=1m$

$\Rightarrow$ Area of square $=(side{)}^2=(1{)}^2=1c{m}^2$

$\Rightarrow$ Area of shaded region = Area of square - Area of $4$ sectors.

$\Rightarrow$ Area of shaded region $=1-0.785=0.215c{m}^2$