Sand is pouring out of a pipe and is forming a conical pile on the ground. The radius of the pile is increasing at a rate of 2 feet per day. The height is always 1 2 of the radius. When the pile has a radius of 18 feet, a) the Volume is 3053.628059 Correct cubic feet b) the rate of change of the VOLUME is Incorrect cubic feet per day..

Explanation:

Rate of Change

The volume of a cone of radius r and height h is given by

The height is said to be 1/2 of the radius, thus

a) Knowing r=18 feet, the volume is

b) The rate of change of the volume is computed by taking the derivative of both sides respect to the time

Where r' is the given rate of change of the radius: 2 feet/day.

Now we compute