Question

A copper wire when bent in the form of a square encloses an area of 484 cm². The same wire is not bent in the form of a circle. Find the area enclosed by the circle.

Answer 1

Area of the circle = 484 cm²
Area of the square = ${\mathrm{Side}}^2$
$$\begin{gathered} \Rightarrow 484={\mathrm{Side}}^2 \\ \Rightarrow {22}^2={\mathrm{Side}}^2 \\ \Rightarrow \mathrm{Side}=22\mathrm{cm} \end{gathered}$$
Perimeter of the square = $4\times \mathrm{Side}$
Perimeter of the square = $4\times 22$
= 88 cm
Length of the wire = 88 cm
Circumference of the circle = Length of the wire = 88 cm
Now, let the radius of the circle be r cm.
​Thus, we have:
​ $$\begin{gathered} 2\mathrm{\pi r}=88 \\ \Rightarrow 2\times \frac{22}{7}\times \mathrm{r}=88 \\ \Rightarrow \mathrm{r}=14 \end{gathered}$$

Area of the circle = ${\mathrm{\pi r}}^2$
$$\begin{gathered} =\frac{22}{7}\times 14\times 14 \\ =616{\mathrm{cm}}^2 \end{gathered}$$

Thus, the area enclosed by the circle is 616 cm².