Calculating Rate of Change for Sphere Volume and Surface Area

[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

 

[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.

 

[HallsofIvy]

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

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.

 

[freman1075]

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.

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

i just divide the two?

 

[lizzie]

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

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

 

[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.

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

i just divide the two?

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!

 

[lizzie]

ok sorry hallsofivy

 

[Gasim]

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