Question

A circular piece of wire is converted into a square of side $6.25cm$. If there is no loss or gain in its length, then the radius of the circular wire is _________ (approximately).

• A. $3.5cm$
• B. $3.98cm$
• C. $4.0cm$
• D. $4.2cm$

Answer 1

The correct option is B $3.98cm$

A circular piece of wire is converted into a square,

Perimeter of circle made by wire$=$ Perimeter of square made by wire

$\Rightarrow 2\pi r=4a$ (where $a$ is the length of the side of square)

$\Rightarrow 2\times 3.14\times r=4\times 6.25cm$ [Since, $\pi =3.14$ (Approximately)]

$\Rightarrow r=\frac{4\times 6.25cm}{2\times 3.14}$

$\Rightarrow r=\frac{2\times 625cm}{314}$

$\Rightarrow r=\frac{625cm}{157}$

$\Rightarrow r=3.98cm$

Hence, Option B is correct.