Question

a wire is in the form of square of side 27.5cm . It is straightened and bent in the form of circle , find the area of the circle.​

Answer 1

As one side = 27.5 cm

=> Perimeter of 4 x 27.5 => 110 cm

Now, C = 2πr

=> 110 = 2πr

=> r = 110/2π = 55/π cm

Also as area = πr²

=> π(55/π)²

=>3025/π cm²

=> 962.9 cm²

Answer 2

As we know that the data given below is provided in the question,

In the above question, it is given that,

It is given that a wire is in the form of a square of side 27.5cm.

It is straightened and bent in the form of a circle.

Here we have to find the area of the circle.

We have to use the formula of the perimeter.

Thus, Perimeter = total length =4 x side=$4\times 27.5 =110cm$.

Now,

The circumference of a circle will be equal to the perimeter of the square.

$\begin{array}{l}\Rightarrow \quad 2 \pi \mathrm{r}=110 \mathrm{~cm} \\\Rightarrow \mathrm{r}=\frac{110 \times 7}{44}=17.5 \mathrm{~cm}\end{array}$

Therefore the Area of a circle is $=\pi r^{2}$

$=\pi \times 17.5^{2} \\=962.11cm^{2}$

Hence the area of a circle is $962.11cm^{2}$