How fast is the height of the pile increasing when the pile is 11 feet high?

Question

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 circular cone whose base diameter and height are always the same.

my work so far:

v=1/3pir^2h

dv/dt=30

diameter= height

r=5.5 ???

Answer 1

hello jessica,

you are in right track.

here d=h

ie. 2r=h

r=h/2 = 11/2

now

Volume = (1/3)*∏*r²*h

=> dv/dt = (1/3)*∏*(11/2)²*(dh/dt)

=> 30 = (1/12)*∏*121*dh/dt

=>dh/dt = 360/(121*∏)

=> dh/dt = 0.947 m/s

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