A wire is bent to form a square enclosing an area of 484 cm2.

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Question:

A wire is bent to form a square enclosing an area of 484 cm2.Using the same wire, a circle is formed. Find the area of the circle.

Solution:

Area of the circle = 484 cm2

Area of the square $=\operatorname{Side}^{2}$

$\Rightarrow 484=$ Side $^{2}$

$\Rightarrow 22^{2}=$ Side $^{2}$

$\Rightarrow$ Side $=22 \mathrm{~cm}$

Perimeter of the square $=4 \times$ Side

Perimeter of the square $=4 \times 22$

$=88 \mathrm{~cm}$

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:

$2 \pi \mathrm{r}=88$

$\Rightarrow 2 \times \frac{22}{7} \times \mathrm{r}=88$

$\Rightarrow \mathrm{r}=14$

Area of the circle $=\pi \mathrm{r}^{2}$

$=\frac{22}{7} \times 14 \times 14$

$=616 \mathrm{~cm}^{2}$

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

 

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