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Sav [38]
3 years ago
7

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 circu

lar 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?
Physics
1 answer:
Alona [7]3 years ago
7 0

Answer:

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,

V=\pi \times \left ( \frac{h^{2}}{4} \right )\times h

V=\pi \times \frac{h^{3}}{4}

Differentiate both sides with respect to h

dV/dh = \frac{\pi }{4}\times 3h^{2}\times \frac{dh}{dt}

by substituting the values

30=\frac{3\times3.14}{4}\times 15\times 15\times \frac{dh}{dt}

dh/dt = 0.0566 feet / min

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