Originally Posted by

**OnMyWayToBeAMathProffesor** I totally blanked on this. I need to find the derivative of the volume of a hemispherical balloon. From the picture i can tell that the volume, $\displaystyle v$=$\displaystyle \pi r^2h$$\displaystyle +$$\displaystyle \frac{4}{3}\pi (r^3)$. For some reason I totally blanked on how to get the derivative of a sphere and cylnder. This is what i got, but I am not sure it is correct. Could someone double check please? Thanks

$\displaystyle v'$=$\displaystyle (\pi)(2r)(\frac{dr}{dt})h+$$\displaystyle 4\pi(r^2)(2\frac{dr}{dt})$

I think i messed up somewhere but not sure where, just as a clarification, $\displaystyle \frac{dr}{dt}$ is the rate of change of the radius in relation to time.

Thanks for helping!