Question

A wire bent in the form of a circle of radius $42cm$ is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by :

• A. $11:12$
• B. $21:33$
• C. $22:33$
• D. $14:11$

Answer 1

Answer: (D)

$14:11$

Length of wire =$2\pi \times 42=84\pi cm$
Let x be the side of the square
We have
$4\times =84\pi$
$\times =21\pi$
Area of the circle : Area of the square
$=\pi {\left(42\right)}^2:{\left(21\pi \right)}^2$
$\pi$ $\times 42\times 42:21\times 21\times$ $\pi$ x $\pi$
=$4:$ $\pi$
$=4:\frac{22}{7}$
= $14:11$