hmm does anyone know how to get the picture to show up ? with out having to click on it ?
For the hollow cylinder shown, assume that R and r are increasing at a rate of 2 m/s, and h is decreasing at a rate of 3 m/s. at what rate is the volume changing when R= 7m and r =4m and h = 5m ?
please help me on the path to solving this problem. I'm sorry the picture isn't perfect.
you can multiply it all out but you still will have to use the product rule.
this solid is a large cylinder with a smaller cylindrical "hole" in it ...
as I stated earlier, once you get the derivative w/r to time sub in your given values for R, r, h, and their respective rates of change to determine dV/dt.
your derivative is incorrect. are you familiar with the technique of implicit differentiation in solving related rates problems? It is important that you clearly understand that R, r, and h are all implicit functions of time.
note the following derivative for the first term on the right side of the equation
Ok is dh/dt equivilant to writing h prime ? ok I understand that now, so when I solve for any related rates problem I use implicit differentiation. ok so now the rate values would be substituted with the R prime h prime and r prime variables, or the dR/dt, dh/dt and dr/dt correct ?