If each edge of a cube is increased by $50\%$, by what percent does its volume increase?

If each edge of a cube is increased by $50\%$, by what percent does its volume increase?
  1. $50\%$
  2. $150\%$
  3. $237.5\%$
  4. $125\%$

Solution

New edge $= 1.5 a$. New volume $= (1.5)^{3} a^{3} = 3.375 a^{3}$. Increase $= 2.375 a^{3}$, i.e. $237.5\%$.

Asked in: IMO

Practice more MENSURATION questions on Aicharya