Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always the same. how fast is the height of the pile increasing when the pile is 15 feet high?

dh/dt = 0.0566 feet / min

Explanation:

Volume per second, dV/dt = 30 cubic feet per minute

Diameter of cone = height of cone = h

at h = 15 feet, dh/dt = ?

Volume of cone is

V = πr²h

where, r be the radius of cone

According to question

radius of cone = half of diameter of cone = h /2

So,

Differentiate both sides with respect to h

by substituting the values

dh/dt = 0.0566 feet / min

answer: 0

explanation: im   14

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