Question

A wire is in the form of a circle of radius $35\mathrm{cm}$. It is now bent in the form of a square, Find the area of the square.

Answer 1

Step 1: Determine the circumference of the circle.

The circumference of the circle $\left(C\right)$ is calculated by $C=2\mathrm{\pi r}$ where $r$ represents the radius of the circle.

$\begin{array}{rcl}& \Rightarrow & C=2\mathrm{\pi }\times 35\\ & =& 70\mathrm{\pi }\mathrm{cm}\end{array}$

Step 2: Determine the area of the square.

The perimeter of a square $\left(P\right)$ is calculated by $P=4s$ where $s$ represents the sides of the square.

A circular wire is now bent in the form of a square.

The circumference of the circle $C$ is equal to the perimeter of the square $P$.

$$\begin{gathered} P=70\mathrm{\pi } \\ \Rightarrow 4\mathrm{s}=70\mathrm{\pi } \\ \Rightarrow \mathrm{s}=17.5\mathrm{\pi }\mathrm{cm} \end{gathered}$$

The area of the square is calculated by $A=s^2$. The value of $\mathrm{\pi }$ is $\frac{22}{7}$.

$\begin{array}{rcl}A& =& {\left(17.5\mathrm{\pi }\right)}^2\\ & =& 17.5\times 17.5\times \frac{22}{7}\times \frac{22}{7}\\ & =& 2.5\times 2.5\times 22\times 22\\ & =& 3025{\mathrm{cm}}^2\end{array}$

Hence, the area of the square is $3025{\mathrm{m}}^2$.