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A steel wire when bent in the form of a square encloses an area of $121 cm 2$ . If the same wire is bent in the form of a circle, find the area of the circle.

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154 c m 2

135 c m 2

140 c m 2

175 c m 2

answer is A.

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Detailed Solution

Given a steel wire when bent in the form of a square encloses an area of

121 cm 2

.
Area of square with side length a is,

A = a 2 ⇒ 121 = a 2 ⇒ a = 11

The perimeter of the square is,

P = 4 × s i d e ⇒ P = 4 × 11 ⇒ P = 44 c m

The perimeter of square is equal to circumference of circle.
The circumference of circle is,

C = 2 π r ⇒ 2 × 227 × r = 44 ⇒ r = 44 × 7 2 × 22 ⇒ r = 7 c m

The area of circle is,

A = π r 2 ⇒ A = 227 × 7 × 7

⇒ A = 22 × 7

⇒ A = 154 c m 2

Therefore, the area is

154 c m 2

.
Hence, option 1 is correct.

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