Question

Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)

Answer 1

Answer:

0.42ft/mn

Step-by-step explanation:

we have the following information to answer this question

dv/dt = 40 feet

height = 11 ft

volume = 1/3πr²h

= 1/3π(h/2)²h

= 1/3πh³/4

= πh³/12

dv/dt = π3h²/12

= πh²/4

dh/dt = 4/πh²dv/dt

= 4(40)÷22/7(11)²

= 160/380.29

= 0.42 ft/min

The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets