Question

A steel wire when bent in the form of a square encloses an area of 121 cm². The same wire is bent in the form of a circle. find the area of the circle.

Answer 1

Let a be one side of the square.
Area of the square = 121 cm² (given)
⇒ a² = 121
⇒ a = 11 cm (since 11 × 11 = 121)
Perimeter of the square = 4 × side = 4a = (4 × 11) cm = 44 cm
Length of the wire = Perimeter of the square
= 44 cm
The wire is bent in the form of a circle.
Circumference of a circle = Length of the wire
∴ Circumference of a circle = 44 cm
⇒ $2\mathrm{\pi r}=44$
⇒ $\left(2\times \frac{22}{7}\times r\right)=44$
⇒ r = $\left(\frac{44\times 7}{2\times 22}\right)$= 7 cm
∴ Area of the circle = ${\mathrm{\pi r}}^2$
= $\left(\frac{22}{7}\times 7\times 7\right)$ cm²
= 154 cm²