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Numerade Educator

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Problem 29 Medium Difficulty

Gravel is being dumped from a conveyor belt at a rate of $ 30 ft^3/min, $ and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is $ 10 ft $ high?

Answer

$0.38 \mathrm{ft} / \mathrm{min}$

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Video Transcript

we know the volume of a cone as pi r squared times h over three. We know that two are is H. Therefore we have high times h over too squared times H Divide by three which gives us V is Hi, it's cubed over 12 which gives us Devi over. DT. There's pie H squared over four times d h over d t now plugging in DV over ditches 30 30 is part of times 10. Remember h is 10 feet, so pi times 10 square divide by four times d h over DT gives us d h over DT is equivalent to sex over five pie units or feet per minute.