A very similar question was asked here. Read over the reply and then try your question again.
No idea what to do here, and all help is appreciated.
A coffee filter has the shape of an inverted cone. Water drains out of the filter at a rate of 10 cm^3/min. When the depth of the water in the cone is 8 cm, the depth is decreasing at 2 cm/min. What is the ratio of the height of the cone to its radius?
Help.
Well, I understood what was happening, but I don't know how to take what was applied to that problem and use it to find a radius, which was given in that one. Please also bear in mind I am no where near your level of math education, and my perception into all of this is much more limited. I apologize for such things.
Since you're dealing with a related rates problem, the chain rule is the key:
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When h = 8, cubic cm per minute and cm per minute.
Therefore when h = 8: .
Let the radius of the conical volume be x when h = 8. Draw a side view of the filter and use similar triangles:
.
Therefore:
.
Therefore, when h = 8, .
Substitute into and solve for the required ratio.
There are probably careless mistakes in the above - check for them. The method is what matters.