Question

Sand is pouring from a pipe at the rate of 12 cm³/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

Answer 1

The volume of a cone (V) with radius (r) and height (h) is given by,

The rate of change of volume with respect to time (t) is given by,

Hence, when the height of the sand cone is 4 cm, its height is increasing at the rate of 1/48π cm/s.