Gravel is being dumped from a conveyor belt at a rate of 20 ft3 /min and its coarseness is such that it forms a pile in the shap
e of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 15 ft high
1 answer:
Answer:
The height of the pile is increasing at the rate of 
Step-by-step explanation:
Given that :
Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min
i.e 
we know that radius r is always twice the diameter d
i.e d = 2r
Given that :
the shape of a cone whose base diameter and height are always equal.
then d = h = 2r
h = 2r
r = h/2
The volume of a cone can be given by the formula:




Taking the differentiation of volume V with respect to time t; we have:


we know that:

So;we have:



The height of the pile is increasing at the rate of 
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