Multiple choice

A cord in the form of a square encloses the area 'S' $cm^2$. If the same cord is bent into the form of a circle, then the area of the circle is

  1. $\frac{\pi s^2}{4}$
  2. $4\pi s^2$
  3. $\frac{s}{4\pi }$
  4. $\frac{4s}{\pi }$
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D Correct answer
Explanation

Perimeter of square = 4a = C (circumference of circle). Area of square S = a^2, so a = sqrt(S). Circumference C = 4*sqrt(S). Radius r = C/(2*pi) = 2*sqrt(S)/pi. Area of circle = pi * r^2 = pi * (4S/pi^2) = 4S/pi.

AI explanation

If the square area is s, its side is the square root of s and its perimeter is 4 * sqrt(s). The circumference of the circle equals this perimeter, so 2 * pi * r = 4 * sqrt(s), meaning the radius is 2 * sqrt(s) / pi. The circle area is pi * r^2 = pi * (4 * s) / pi^2 = 4 * s / pi.

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