The height of a cone with semi vertical angle $\pi / 3$ is increasing at the rate of 2 units $/ \mathrm{min}$. The rate at which the radius of the cone is to be decreased so as to have a fixed volume always is

• A

  $\frac{1}{\sqrt{3}}$
• B

  $\frac{1}{\sqrt{2}}$
• Correct answer
  C

  $\sqrt{3}$
• D

  $\sqrt{2}$

Hence, the correct answer is option: 'C'.