calculus question

[larp]

A spherical balloon deflates, losing volume at the rate of 5 cubic cm/second how quickly is the radius shrinking at the moment when the volume is 18 cubic cm

 

[galactus]

Use \(\displaystyle V=\frac{4}{3}{\pi}r^{3}\) for the volume of the balloon.

Thus, \(\displaystyle \frac{dV}{dt}=4{\pi}r^{2}\cdot \frac{dr}{dt}\)

Set V=18 and solve for r.

Now, you have the radius when V=18.

Set dV/dt=-5, sub in the newly found r and solve for dr/dt.