If the radius of a circle is increased by $20\%$, by what percent does its area increase?

If the radius of a circle is increased by $20\%$, by what percent does its area increase?
  1. $20\%$
  2. $40\%$
  3. $44\%$
  4. $60\%$

Solution

Area $\propto r^{2}$. New area factor $= (1.20)^{2} = 1.44$, an increase of $44\%$.

Asked in: IMO

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