# Rate of Change Problem

1. Sep 2, 2008

### freman1075

hi everyone,
i am having trouble with this rate of change question.
I need to find the rate of change of a sphere with a volume of V= 4/3*pi*r^3 in respect to it's surface area of A= 4*pi*r^2
can anyone give me a hand?
Thanks

2. Sep 2, 2008

### robert Ihnot

Since the surface area- the derivative of the volume-is A=4*pi*r^2, it would seem that change there would be the derivative, 8*pi*r.

3. Sep 3, 2008

### HallsofIvy

Staff Emeritus
So you want to find dV/dA? Use the chain rule dV/dr= (dV/dA)(dA/dr) so dV/dA= (dV/dr)/(dA/dr). Find dV/dr and dA/dr and divide.

4. Sep 3, 2008

### freman1075

so if dV/dr = 4*pi*r^2
and if dA/dr = 8*pi*r

i just divide the two?

5. Sep 3, 2008

### lizzie

dv/dr = 4/3*pi*3*r^2 = 4*pi*r^2

da/dr = 4*pi*2*r = 8*pi*r

dv/da = dv/dr * dr/da = r/2

6. Sep 3, 2008

### HallsofIvy

Staff Emeritus
Well, that is what I said in the post you quoted!

Lizzie, when a person asks for help, please do not just do the problem for them!

7. Sep 5, 2008

### lizzie

ok sorry hallsofivy

8. Sep 18, 2008

### Gasim

to find the rate of change for designing of catalytic oxidation converter
SO2+0.5O2 <---->SO3