The volume of a cylinder increases at a rate of 324cm cube per second. The height, h cm of the cylinder is twice the radius, r cm. Find the rate of change in radius when the radius is 6cm.(use 3over2 pai)

Answer 1

v = πr^2h
dv/dt = 2πrh dr/dt + πr^2 dh/dt

Now just plug in your numbers to get dr/dt

Note that since h=2r, dh/dt = 2 dr/dt

Or, since h=2r,

v = πr^2h = 2πr^3
dv/dt = 6πr^2 dr/dt