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

1.	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 cm22. 254 cm23. 100 cm24. 154 cm2
Answer» 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.

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 cm22. 254 cm23. 100 cm24. 154 cm2

Answer» 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.

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