# Math Help - Need help with related rate problem.

1. ## Need help with related rate problem.

How fast is the surface area of a spherical balloon increasing if the radius is 7 in and the volume is increasing at the rate of 5 cu in/sec?

I'm not sure how to solve this one as S=4*pi*r^2 does not take into account volume.

2. Originally Posted by swatpup32
How fast is the surface area of a spherical balloon increasing if the radius is 7 in and the volume is increasing at the rate of 5 cu in/sec?

I'm not sure how to solve this one as S=4*pi*r^2 does not take into account volume.
You do know that

$V=\frac{4}{3}\pi r^3$ so taking the deriviative with respect to t gives

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

We were given that value of $\frac{dV}{dt}=5$

so we can solve for $\frac{dr}{dt}$

This should get you started, happy hunting

3. So the dr/dt from v = 4/3*pi*r^3 will be the input for dr/dt from s=4*pi*r^2.

correct?

4. Originally Posted by swatpup32
So the dr/dt from v = 4/3*pi*r^3 will be the input for dr/dt from s=4*pi*r^2.

correct?
Exactly!!