Question

A metal wire when bent in the form of a square encloses an area 121 cm². If the same wire is bent in the form of a circle, then its area is:
1. 308 cm²
2. 254 cm²
3. 100 cm²
4. 154 cm²

Answer 1

Correct Answer - Option 4 : 154 cm²

Given:

A metal wire when bent in the form of a square encloses an area 121 cm2.

Formula used:

Area of circle = \(\pi \) × r²

Radius = r , \(\pi \) = 22/7

Calculation: 

Side of square = √ area

⇒ √ 121

⇒ 11 cm

Length of the wire or circumference of the wire = 4 × side

⇒ 4 × 11

⇒ 44 cm

Circumference of the circle = 2\(\pi \)r

⇒  2\(\pi \)r = 44

⇒ r = (44 × 7)/(22 × 2)

⇒ r = 7 cm

Area of the circle =  \(\pi \) × r2

⇒ (22/7) × 7 × 7

⇒ 154 cm²

∴ Area of the circle is 154 cm².