Volume Rate of Change: Understanding Math

[karush]

View attachment 1561

on b) I think this is the point they wanted us to get
hope answers are correct its an even problem # so no ans in bk.

 

[MarkFL]

Re: volume rate of change

Your results for part a) are correct. :D

In your working, where you evaluate \(\displaystyle \frac{dV}{dt}\) for the given values of $r$, you should have replaced \(\displaystyle \frac{dr}{dt}\) with \(\displaystyle 3\,\frac{\text{in}}{\text{min}}\) instead of \(\displaystyle 3\text{ in}\). Also, I think what they are looking for in part b) is that \(\displaystyle \frac{dV}{dt}\) is proportional to the square of $r$. Thus it changes quadratically, not exponentially.