Related Rates Problem: Calculating Sand Leak Rate from Conical Pile Height

[regnar]

Hi, I've tried this too many ways and i can't seem to figure it out. the question is:
As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which the sand is leaking out when the altitude is ten inches.

It would be great help, if someone could help me. Thank you

 

[jav]

The first step in these type of problems is to identify what you are looking for symbolically. In this case you are trying to solve for the rate at which sand is leaking from the container. So write out what this means in terms of derivatives.

The second step is to find an equation relating what you know to what you are trying to figure out... (Think volume of a cone)

Once you have these pieces, the problem should be fairly straight forward by manipulating your equation to get what you are after in the first step.

 

[Mark44]

Regarding the conical pile, its cross-section is a triangle. Use that triangle to get a relationship between the height of the pile and its diameter (the base of the triangle).

 

[jav]

Regarding the conical pile, its cross-section is a triangle. Use that triangle to get a relationship between the height of the pile and its diameter (the base of the triangle).

I think the relationship is given (assuming altitude and height are the same quantity). The problem says "it forms a conical pile whose altitude is always the same as its radius."