Differential Calculus Word Problem

[shadow15]

How do you solve this?

Sand is being poured from a dumping truck and forms a conical pile with its height equal to one third the base diameter. If the truck is emptying at the rate of 720 cubic feet a minute and the outlet is five feet above the ground, how fast is the pile rising as it reaches the outlet?

I tried many different methods and pictures, but can't seem to reach the given answer (4.07 ft./min.). What are the steps I need to take in order to get that answer?

Thanks in advance

 

[Whovian]

First, find a relationship between the height of the height and the volume. This should be fairly basic geometry.

Now differentiate both sides with respect to time, use the chain rule if necessary, plug in a few values, and solve.

 

[berkeman]

How do you solve this?

Sand is being poured from a dumping truck and forms a conical pile with its height equal to one third the base diameter. If the truck is emptying at the rate of 720 cubic feet a minute and the outlet is five feet above the ground, how fast is the pile rising as it reaches the outlet?

I tried many different methods and pictures, but can't seem to reach the given answer (4.07 ft./min.). What are the steps I need to take in order to get that answer?

Thanks in advance

You *must* show your work toward a solution. It is not enough to say you have tried it and have not been able to solve it.

Please use the hints provided, and show us your work on this question.

 

[STEMucator]

Remember, the volume of a cone is V = (π/3)r²h. It's diameter is just 2r, where r is the radius. It's height though will be (1/3)(diameter). Using this information will allow you to construct the relationship between your info.

Then, think about dv/dt, which is really what the question is asking for (i.e how fast is the volume of the cone growing). You're given two useful pieces of info that will allow you to formulate a formula for this.

Then I mean... plug and chug right?