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

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

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