Sand falls from a conveyor belt at a rate of 9 m cubed divided by min onto the top of a conical pile. the height of the pile is always three-eighths of the base diameter. how fast are the height and the radius changing when the pile is 5 m high?

for height = 1.07mm/S

for radius=1.43mm/S

Explanation:

Hello!

To solve this problem we must use the following steps, the whole detailed procedure is attached.

1. Find the volumetric flow of sand in m ^ 3 / s, this data says it in the problem.

2. Pose the equation for the volume of a cone and the equation that relates the height to the diameter of the problem, use these two equations to find a relationship between the volume and the radius.

3. Derive both sides of the equation with respect to time considering that the change in volume with respect to time is the volumetric flow found in the first point.

4. Find the change of the radius with respect to time for a height of 5m.

5. Find the change in height with respect to time taking into account the relationship of the diameter with the height.

b.

explanation:

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