# related rates calculus 1

gravel is being dumped from a conveyor belt at a rate of 15 ft^3/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 10ft

1. 👍 1
2. 👎 0
3. 👁 1,714
1. height ------- h

V = (1/3)π r^2 h
= (1/3)π (h^2/9)(h) = (π/27) h^3

dV/dt = (π/9) h^2 dh/dt
for the given data:
15 = π/9 (100)dh/dt
dh/dt = 135/(100π) ft/hr

1. 👍 0
2. 👎 0
2. How did you get "dh/dt = 135/(100π) ft/hr?"

That's the only part I'm confused about.

1. 👍 0
2. 👎 0
3. from
15 = π/9 (100)dh/dt

I multiplied both sides by 9/(100π)
which left me with dh/dt on the one side
and 15(9/(100π) ) or 135/(100π) on the other side

1. 👍 0
2. 👎 0
4. oh okay, I ended up getting .43ft/hr. I'm 99% sure that's the correct answer.

Thanks for clearing that up for me, I'm really ing at related rates, so I'm doing all the problems I can.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### 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

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

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

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

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

2. ### 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

3. ### 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

4. ### math

In 2 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long

1. ### 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

2. ### 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

3. ### 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

4. ### 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