# Calculus

Gravel is being dumped from a conveyor belt at a rate of 25 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 6 ft high? (Round your answer to two decimal places.)

1. 👍 0
2. 👎 0
3. 👁 808
1. since h = 2r, r = h/2
v = pi/3 r^2h = pi/12 h^3
So,
dv/dt = pi/4 h^2 dh/dt

When h=6, we have

25 = 9pi dh/dt

Now just do the math

1. 👍 0
2. 👎 0
2. derp

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

Dana loads luggage into an airplane using a conveyor belt tilted at an angle of 20°.She places a few pieces of luggage on the belt before it starts to move, then she turns the belt on. It takes the belt 0.70 s to reach its top

2. ### Related Rates

Gravel is being dumped from a conveyor belt at a rate of 10 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. How fast is the height of the pile

3. ### Physics

A 0.075 kg ball in a kinetic sculpture moves at a constant speed along a motorized conveyor belt. The ball rises 1.32 m above the ground. A constant frictional force of 0.350 N acts in the direction opposite the conveyor belt's

4. ### Physics

A 20 kg crate is placed on a horizontal conveyor belt. The materials are such that us = 0.47 and uk = 0.21. What is the maximum acceleration the belt can have without the crate slipping? If acceleration of the belt exceeds the

1. ### calculus

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approx­ imately three times the altitude. At what rate is the

2. ### Calculus - Rate of Change

Can someone explain how to solve this problem? Sand is being dumped on a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is

3. ### Calc

Gravel is being dumped from a conveyor belt at a rate of 10 ft^3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the

4. ### Engineering Economics

A granary has two options for a conveyor used in the manufacture of grain for transporting, filling, or emptying. One conveyor can be purchased and installed for \$70,000 with \$3,000 salvage value after 16 years. The other can be

1. ### Calculus

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile

2. ### physics

A box is dropped onto a conveyor belt moving at 1.9 m/s. The acceleration of gravity is 9.8 m/s^2. If the coefficient of friction between the box and the belt is 0.8, what distance does the box move before it moves without

3. ### Math

Gravel is being dumped from a conveyor belt at a rate of 50 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. How fast is the height of the pile

4. ### Physics

A piece of luggage is being loaded onto an airplane by way of an inclined conveyor belt. The bag, which has a mass of 10.0 kg, travels 6.50 m up the conveyor belt at a constant speed without slipping. If the conveyor belt is