Question

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

• A. $22\mathrm{cm}$
• B. $14\mathrm{cm}$
• C. $11\mathrm{cm}$
• D. $7\mathrm{cm}$

Answer 1

The correct option is B

$14\mathrm{cm}$

Explanation for the correct option:

Radius of the circle obtained by bending

Side of square $22\mathrm{cm}$

The perimeter of a square and the circumference of a circle are equal because the length of the wire is the same.

$$\begin{gathered} \mathrm{The}\mathrm{perimeter}\mathrm{of}\mathrm{square}=\mathrm{circumference}\mathrm{of}\mathrm{a}\mathrm{circle}. \\ \Rightarrow 4\times \mathrm{side}=2\mathrm{\pi }\times r \\ \Rightarrow 4\times 22=2\times \frac{22}{7}\times r\mathbf{}\left[\because \pi =\frac{22}{7}\right] \\ \Rightarrow r=\frac{4\times 22\times 7}{2\times 22} \\ \therefore r=14\mathrm{cm} \end{gathered}$$

So, the radius of the circle is $14\mathrm{cm}$.

Hence, the correct option is option (B).