How to find rate of change of radius given rate of change for volume? A balloon is being filled with helium at the rate of $4\frac{ft^3}{min}$. The rate, in feet per minute, at which the radius is increasing when the radius is $2$ feet is ($V=\frac43 \pi r^3$):  ?
I know rate of change has to do with derivatives but after finding the derivative of the volume equation I don't know what to do next.
I don't want the answer to this specific problem, I don't understand how to do these specific problems in general.
 A: hint: $\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt}$, and you are given: $\dfrac{dV}{dt} = 4, r = 2$, can you find $\dfrac{dr}{dt}$ ?
A: There is always something I call, "the side problem," in these.  Usually, there is some relationship between the geometrical parts of the problem.  For instance, in a conical tank that's filling up, if you take the cross section of the tank, you get a triangle, and the "side problem" turns out to be about ratios in similar triangles.  A big part of doing related rates problems is implicit differentiation and then reducing the number of rates that we're concerned with by doing something that eliminates one of the variables, specifically, relates the height of something to the radius when we are concerned with dV/dt when it relates to a radius, and stuff like that.  
In general, implicit differentiation and looking for a side relationship that cuts down on the number of variables and rates by putting them in terms of a single rate is a good high-level approach to these.
