question_answer

If the difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is\[26.705\text{ }{{m}^{2}}\]. Find the radius of the circular swimming tank. \[(\pi =3.143,\,\,\sqrt{3}=1.732)\]

A)  4 cm                          

B)  7 cm              

C)  11 cm                        

D)  9 cm

Correct Answer: B

Solution :

For regular hexagon, \[\Delta OAB\]is an equilateral triangle.                       \[\therefore \] Side of hexagon             = radius of circle = r (say)         Area of hexagon \[=6\times \]Area of \[\Delta OAB\]             \[=6\times \frac{\sqrt{3}}{4}\times {{r}^{2}}\] Area of circle \[=\pi \,{{r}^{2}}\] According to question,             \[\pi {{r}^{2}}-\frac{6\sqrt{3}}{4}\times {{r}^{2}}=26.705\] \[\Rightarrow \]    \[{{r}^{2}}\left( 3.143-\frac{3}{2}\times 1.732 \right)=26.705\] \[\Rightarrow \] \[{{r}^{2}}(0.545)=26.705\,\,\Rightarrow \,\,{{r}^{2}}=49\,\,\Rightarrow \,\,r=7\]