question_answer

A wire bent in the form of a circle of radius 42 cm is again bent in the form of a square. What is the ratio of the regions enclosed by the circle and the square?

A) \[11:12\]                      

B)  \[21:33\]

C) \[22:33\]                      

D)  \[14:11\]

Correct Answer: D

Solution :

\[2\pi \times 42\]length becomes perimeter of square. Area (Circle) \[=\pi \times {{42}^{2}}\] Side of square \[=\frac{2\pi \times 42}{4}=21\pi \Rightarrow \] Area (square) \[{{\left( 21\pi  \right)}^{2}}\] \[\therefore \]\[\frac{Area\,\left( circle \right)}{Area\,\left( Square \right)}=\frac{\pi \times {{42}^{2}}}{{{\pi }^{2}}\times {{21}^{2}}}=\frac{4}{\pi }=\frac{4}{22/7}=\frac{14}{11}\]