Question
A wire is bent to form a square enclosing an area of $484m^2$. Using the same wire, a circle is formed. Find the area of the circle.
✓
Answer
Area of a square formed $= 484m^2$
$\Rightarrow \text{(Side)}^2 = 484$
$\Rightarrow \text{Side}=\sqrt{484}\text{m}=22\text{m}$
$\therefore$ Perimeter of a square $= 4 \times $ side$ = 4 \times 22 = 88m$
Let r be the radius of the circle formed
Now,
circumference of a circle = Perimeter of square
$\Rightarrow2\times\frac{22}{7}\times\text{r}=88$
$\Rightarrow\text{r}=\Big(88\times\frac{7}{44}\Big)=14\text{m}$
$\therefore$ Area of the circle $=\pi\text{r}^2=\Big(\frac{22}{7}\times14\times14\Big)\text{m}^2=616\text{m}^2$
$\Rightarrow \text{(Side)}^2 = 484$
$\Rightarrow \text{Side}=\sqrt{484}\text{m}=22\text{m}$
$\therefore$ Perimeter of a square $= 4 \times $ side$ = 4 \times 22 = 88m$
Let r be the radius of the circle formed
Now,
circumference of a circle = Perimeter of square
$\Rightarrow2\times\frac{22}{7}\times\text{r}=88$
$\Rightarrow\text{r}=\Big(88\times\frac{7}{44}\Big)=14\text{m}$
$\therefore$ Area of the circle $=\pi\text{r}^2=\Big(\frac{22}{7}\times14\times14\Big)\text{m}^2=616\text{m}^2$
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