Multiple choice

If the circumference of a circle is increased by $20\%$. then Its area will be increased by.

  1. $44\%$
  2. $32\%$
  3. $40\%$

  4. none of these
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A Correct answer
Explanation

Circumference C = 2*pi*r. If C increases by 20%, r increases by 20%. Area A = pi*r^2. New area = pi*(1.2r)^2 = 1.44*pi*r^2. Increase = 44%.

AI explanation

Let the initial circumference be C, making the initial radius r equal to C divided by 2 times pi. Since circumference increases by 20 percent, the new radius is 1.2r, meaning the new area is pi times (1.2r) squared, which is 1.44 pi r squared. The initial area was pi r squared, so the increase is 0.44 pi r squared, representing a 44 percent increase in area.

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