6th Class
Mathematics
Mensuration
Question Bank
Mensuration Basics
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)\[={{(21\pi )}^{2}}\] \[\therefore \]\[\frac{Area\,\left( circle \right)}{Area\,\left( Square \right)}=\frac{\pi \times {{42}^{2}}}{{{\pi }^{2}}\times {{21}^{2}}}=\frac{4}{\pi }=\frac{4}{22/7}=\frac{14}{11}\]