# Math Help - Derivations

1. ## Derivations

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

i keep getting 7040*pi as my answer.. but its not correct.

please help mee!

2. Originally Posted by calculus shmalculus
Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

i keep getting 7040*pi as my answer.. but its not correct.

please help mee!
of course that's not correct, that's the wrong equation.

recall, the surface area is given by $A = 4 \pi r^2$ and the volume is given by $V = \frac 43 \pi r^3$

3. i know the equations for both..
what i am asking is if i need to derivate the surface area equation and if so ho would i go about doing that..
i have been attempting his problem for a while now..

ugh..
please help..

4. Originally Posted by calculus shmalculus
i know the equations for both..
what i am asking is if i need to derivate the surface area equation and if so ho would i go about doing that..
i have been attempting his problem for a while now..

ugh..
please help..
if you differentiate A implicitly, you will end up with dr/dt as opposed to dV/dt as you wrote.

use the volume equation to find dr/dt, when r = 11

then, use that for dr/dt when you implicitly differentiate the Area equation