Question

A piece of wire, made in the form of a square of side $5.5cm$ is cut and molded in the form of a circle. Find the radius of the circle so formed.

Answer 1

A piece of wire, made in the form of a square is cut and moulded in the form of a circle.

So, the perimeter of the square $=$ Perimeter of circle ………………(1)

Step I: Find the perimeter of the Square.

The side of a square is $5.5cm$

So, Perimeter of square $=4\times side$

$=4\times 5.5$

$=22cm$.

Step II: Find the perimeter of the circle.

Perimeter of circle $=$Circumference of the circle.

So, Perimeter of circle $=2\mathrm{\pi r}$

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

$=\frac{44}{7}\times r$

Step III: Finding the value of $r$.

Substituting the values in (1),

$22=\frac{44}{7}\times r$

Multiplying both sides by $7$,

$22\times 7=\frac{44}{7}\times 7\times r$

$154=44\times r$

Dividing both sides by $44$,

$\frac{154}{44}=\frac{44r}{44}$

Therefore, $r=3.5cm$.

Hence, the radius of the circle so formed is $3.5cm$