A filter filled with liquid is in the shape of a vertex-down cone with a height of 16 inches and a diameter of 24 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 7 cubic inches per second, how fast is the level of the liquid dropping when the liquid is 4 inches deep?

I know that the volume of a cone is $\displaystyle \frac{1}{3} \pi r^2 h$.

From earlier examples I know that I have to somehow rewrite this equation using only one variable, and this is where I always get stuck with these problems. The book gives a hint that the equation can be rewritten

with respect to either the height or radius because the height and radius of the cone is fixed.

The answer to this problem is $\displaystyle \frac{112}{144\pi}$.

Thanks.