Question

A wire, when bent in the form of a square, encloses an area of $196c{m}^2$. If the same wire is bent to form a circle, find the area of the circle.

Answer 1

Area of Square $=196c{m}^2$

$\therefore$ Side of Square $=\sqrt{Area}$

$=\sqrt{196}$

=14 cm

$\therefore$ Perimeter of Square $=4\times 14cm$

i.e. length of wire =56 cm

$\therefore$ Circumference of circle =56 cm

$2\pi r=56$

$2\times \frac{22}{7}\times r=56$

$r=\frac{56\times 7}{2\times 22}$

$r=\frac{98}{11}cm$

$\therefore$ Area of circle enclosed $=\pi r^2$

$=\frac{22}{7}\times \frac{98}{11}\times \frac{98}{11}$

$=\frac{2744}{11}$

$=249.45c{m}^2$