Question

A copper wire when bent in the form of a square encloses an area of 484 cm². If the same wire is bent in the form of a circle, find the area enclosed by it.

Answer 1

Given: A copper wire bent as a square encloses an area of 484 cm².

Step-wise calculation:

1. Side of square 

= `sqrt(484)`

= 22 cm

2. Perimeter (length of wire) 

= 4 × 22

= 88 cm

3. For a circle with circumference C = 88 cm, radius `r = C/(2π)` 

= `88/(2π)` 

= `44/π` cm

4. Area of circle 

A = πr²

= `π (44/π)^2` 

= `1936/π` cm²

5. Numerical approximations:

If `π = 22/7` 

⇒ A = `1936 ÷ 22/7` 

= 616 cm²

If π = 3.14159265

⇒ A = 1936 ÷ 3.14159265

= 616.85 cm²

The area enclosed when the wire is bent into a circle is `1936/π` cm² (≈ 616 cm² using π = `22/7` or ≈ 616.85 cm² using π ≈ 3.1416).