Multiple choice

If the radius of the circle increases by 40% its area will be increased by

  1. $96\%$
  2. $100\%$
  3. $80\%$
  4. $126\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area A = pi * r^2. If r increases by 40%, new radius r' = 1.4r. New area A' = pi * (1.4r)^2 = 1.96 * pi * r^2. The increase is 1.96 - 1 = 0.96, which is 96%.

AI explanation

Using the percentage change formula, the area increases by a + b + (ab/100) when two dimensions change by a% and b%. Substituting the 40% increase for the radius gives 40 + 40 + (40 * 40)/100, which equals 80 + 16. The total area increase is 96%.

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