Gravel is being dumped from a conveyor belt at a rate of 30 ft/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and heght are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 14 it high?

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  0.195 ft/min

Step-by-step explanation:

The rate of change of height is equal to the rate of change of volume, divided by the base area.

  base area = (π/4)d² = (π/4)(14 ft)² = 49π ft² ≈ 153.94 ft²

Then the rate of change of height is ...

  (30 ft³/min)/(153.94 ft²) ≈ 0.19488 ft/min ≈ 0.195 ft/min

That's about 2.34 inches per minute.

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step-by-step explanation:

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