A copper wire when bent in the form of a square encloses an area of 121 cm^2. If the same wire is bent into the form of a circle, find the area of the circle.
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Step-by-step explanation:
Solution :
Let the side of the square be a cm.
Area of square = a² cm².
According to given,
a² = 121
a = √121
a = 11.
The length of the wire
➡ perimeter of the square
➡ 4a cm
➡ 4 × 11 cm
➡ 44 cm.
Let r cm be the radius of the circle.
Circumference of the circle = 2πr.
As the same wire is to be bent into the form of circle,
➡ 2πr = 44
➡ 2 × 22/7 × r = 44
➡ r = 7.
Therefore :
The area of the circle = πr² = (22/7 × 7 × 7) cm² = 154 cm².
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