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