If the circumference of a circle is equal to the perimeter of square then which one of the following...........

Quantitative Aptitude ( CCS) Mensuration 2D

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If the circumference of a circle is equal to the perimeter of square, then which one of the following is correct ?

Area of circle = Area of square

Area of circle ≥ Area of square

Area of circle > Area of square

Area of circle < Area of square

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Explanation:

Let, the radius of a circle = r and the side of a square = a
Given, circumference of a circle = perimeter of a square
⇒ 2πr = 4a
⇒ a = π /2r
= 3.14 /2r = 1.57r
Now, Area of the circle = πr² = 3.14r²
And, Area of the square = a² = (1.57r²) = 2.4649r²
∴ Area of circle > Area of square