I am having a problem getting started on this problem.
Rate of inflation of a balloon. A spherical balloon is inflated at a rate of 10 cubic cm/min. At what rate is the diameter of the balloon increasing when the balloon has a diameter of 5 cm.
For the life of me I cannot figure out what formula to begin with so I can find dd/dt (this is an assumption that it is related to diameter) not sure it could be related to anything else. I am not looking for the problem to be solved just help getting started.
Best Answer
HINT: volume of the balloon($V$) = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi {(\frac{D}{2})}^3=\frac{1}{6}\pi D^3$
and you are given $\frac{dV}{dt}$ and need to find $\frac{dD}{dt}$