Asked by Debbie
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.
Answers
Answered by
Reiny
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
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
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