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.
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
$\displaystyle V=\frac{4}{3}\pi r^3$ so taking the deriviative with respect to t gives
$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$
We were given that value of $\displaystyle \frac{dV}{dt}=5$
so we can solve for $\displaystyle \frac{dr}{dt}$
This should get you started, happy hunting