Question

Gravel is being dumped from a conveyor belt at a rate of 15 ft3/hr and its coarseness is such that it forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of 10 ft

Answer 1

Answer:

0.43 ft/hr

Step-by-step explanation:

dv/dt = 15ft³/hr

Height = 10ft

We are required to get dh/dt

h = 3r

r = h/3

Formula for volume = 1/3πr²h

We put value of h

1/3π(h/3)²h

= 1/3π(h²/9)h

= 1/3πh³/9

= πh³/29

dv/dt = 1/27π.3h²dh/dt

= dv/dt = πh²/9dh/dt

Remember dv/dt = 15

When we put this in we get

dh/dt = 15x9/3.142x10²

= 135/314.2

= 0.43 ft³/hr

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