Question

Question 5

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Find the area of the circle obtained.

(a) $196c{m}^2$
(b) $212c{m}^2$
(c) $616c{m}^2$
(d) $644c{m}^2$

Answer 1

Given, side of a square = 22 cm
The perimeter of square and circumference of circle are equal because the wire has the same length.
According to the question,
Perimeter of square = Circumference of circle
$\Rightarrow 4\times \left(Side\right)=2\times \pi \times r$
$\Rightarrow 4\times 22=2\times \frac{22}{7}\times r$ $[\because \pi =\frac{22}{7}]$
$\Rightarrow r=\frac{4\times 22\times 7}{2\times 22}$
$\Rightarrow r=14cm$
Hence, the radius is 14 cm.
Area of the circle $=\pi r^2=\frac{22}{7}\times 14\times 14=616c{m}^2$ $[\because r=14cm,findabove]$