question_answer 1)

Sand is pouring from a pipe at the rate of 12 cm2/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:

Let r and h be the radius and height of the sand cone respectively.                                     .. (1)       Given :  [V = Volume of sand cone]       Since             [B (1)]                                           Hence height of the sand cone increase at the rate