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