Question

A copper wire when bent in the form of a square encloses an area of 484 sq cm if the same wire is bent in the form of a circle the area enclosed by it is
(Use $\pi =\frac{22}{7}$)

• A. 412 $c{m}^2$
• B. 616 $c{m}^2$
• C. 500 $c{m}^2$
• D. None of these

Answer 1

The correct option is B 616 $c{m}^2$

Area of the square$=484c{m}^2$

$\therefore$ Side of the square $=\sqrt{484}=22cm$

$\Rightarrow$ Perimeter of the square $=4\times 22=88cm$

$\because$ (Circumference of the circle) $=$ (perimeter of the square)

$\Rightarrow 2\pi r=88$

$\Rightarrow 2\times \frac{22}{7}\times r=88$

$\therefore r=\frac{88\times 7}{2\times 22}=14cm$

$\therefore$ Area of the circle $=\pi r^2=\frac{22}{7}\times 14\times 14c{m}^2$

$=616c{m}^2$