Question

A wire is bent into the form of a square of side 27.5 cm. The wire is straightened and bent into the form of a circle. What will be the radius of the circle so formed?
[3 marks]

Answer 1

Length of wire $=$ perimeter of the square
$=27.5\times 4$ cm
$=110$ cm
[1 mark]

When the wire is bent into the form of a circle, then it represents the circumference of the circle which would be 110 cm.

Let $r$ be the radius of this circle
Then, circumference $=$ $2\times \pi \times r$
$\Rightarrow$ 110 $=$ $2\times \frac{22}{7}\times r$
$\Rightarrow$ $r$ $=$ $\frac{110\times 7}{4}$
$\Rightarrow$ $r$ $=$ $17.5$ cm

∴ Radius of the circle formed $=$ $17.5$ cm
[2 marks]