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I need help with this cal 1 related rates question?

Gravel is being dumped from a conveyor belt at a rate of 20 ft^3/min. 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 19 ft high?

Answer 1

Emilia Aguilar

#80/(19^2pi)# ft/min

We know #d=h, =>r=h/2#

So #V=1/3pi(h/2)^2h\ \ \ =>\ \ \ V(t)=pi/12h^3(t)#

Distinguishing between t

#V'(t)=pi/4h^2(t)h'(t)#

We know #V'(t)=20 \ \ AA t\ \ ,\ \ \ h(t_0)=19# So

#20=pi/4*19^2h'(t_0)#

#h'(t_0)=80/(19^2pi)#

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Answer 2

Luke Alvarez

Of course, please provide the specific related rates question you need help with, and I'll be happy to assist you.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.