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What will be the area of a circle, when a steel wire is bent in the form of a square enclosing an area of $121 c m 2$ bent in the form of a circle?

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154

c m 2

200

c m 2

204

c m 2

196

c m 2

answer is A.

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Detailed Solution

To find the area of the circle, we will need to find its radius.
First, we need to find the side of the square from its area.
Area of square

= s i d e 2

121 c m 2 = s i d e 2

112 = s i d e 2

s i d e = 11 c m

Also, we know that both the squares and circles are made from the same length of wire so they will have the same perimeter.
The perimeter of a square is equal to

4 × s i d e

and the perimeter of a circle is

2 π r

4 × s i d e = 2 π r

4 × 11 = 2 × 227 × r

r = 7 c m

Now, we can find the area of the circle using the formula

π r 2

π r 2 = 227 × 72

= 154 c m 2

Hence, option 1 is correct.

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