suppose a balloon used in angioplasty is a 30mm long cylinder, with hemispherical caps at both ends.Determine a relationship between the rate of change in the volume of the balloon and the rate of change of its diameter.
Let the radius of the hemispherical caps be r mm
so the volume would be the sum of a whole sphere and the cylinder, so
V = (4/3)πr^3 + 30πr^2
dV/dt = 4πr^2 dr/dt + 60π dr/dt
= (4πr^2 + 60π) dr/dt