Question

Question 4

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is

(a) 22 cm
(b) 14 cm
(c) 11 cm
(d) 7 cm

Answer 1

Given, side of a square = 22 cm
Perimeter of square and circumference of circle are equal, because the wire has 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.