Originally Posted by

**angrynapkin** So, my textbook only covers implicit diff. as it relates to ellipses and circles. Needless to say, it all went over my head. Now I have a related rates question where I absolutely need to use implicit diff. Here goes:

A water tank has the shape of an inverted cone with a base radius of 4 meteres and a height of 6 meteres. If water is being pumped into the tank at a rate of 3 m^3/min, find the rate at which the water level is rising when the tank is 4 meters deep. Specify the units of your answer.

So I have two triangles, one with measurements given, and one with only height (because radius at 4m deep is currently unknown)

I also have the formula V = 1/3 pi*r^2*h

Now, to set up a proportion to find r?

r 4

-- = --

h 6

6r = 4h, in terms of r

r = 4h/6, substitute the known h

r = 8/3m

If I did everything right, I now know the radius of the cone when height = 4m. However, I'm sure I need to implicitly differentiate the volume formula and I'm not sure how.