A copper wire when bent in the form of a square encloses an area of 272.25 cm². If the same wire is bent into the form of circle, what will be the area enclosed by the wire?

By formula,

Area of square = (side)²

Given,

Area of square = 272.25 cm².

∴ (side)² = 272.25

⇒ side = $\sqrt{272.25}$

⇒ side = 16.5 cm.

Perimeter of square = 4 × side = 4 × 16.5 = 66 cm.

Circumference of circle of same wire = Perimeter of square of same wire.

Let radius of circle be r cm.

$\therefore 2πr = 66 \\[1em] \Rightarrow 2 \times \dfrac{22}{7} \times r = 66 \\[1em] \Rightarrow 44 \times r = 66 \times 7 \\[1em] \Rightarrow r = \dfrac{66 \times 7}{44} \\[1em] \Rightarrow r = \dfrac{21}{2} = 10.5 \text{ cm}.$

By formula,

Area of circle = πr²

= $\dfrac{22}{7}$ × (10.5)²

= $\dfrac{22}{7}$ × 10.5 × 10.5

= 22 × 1.5 × 10.5

= 346.5 cm².

Hence, area enclosed by the wire in the form of a circle = 346.5 cm².