Question:
Sand is pouring from a pipe at the rate of $18 \mathrm{~cm}^{3} / \mathrm{s} .$ The falling sand forms a cone on the ground in such a way that the height of the cone is one-sixth of the radius of the base. How fast is the height of the sand cone increasing when its height is $3 \mathrm{~cm}$ ?
Solution:
