The trunk of a tree is approximately cylindrical in shape and has a diameter of 1 m when the height is 15m. If the radius is inreasing at 3mm/a and the height is increasing at 0.4 m/a, find the rate of increase of the volume of the trunk.
using related triangles i got r = h/30 and h=30r
and using the volume of a cylinder i got V = ( pi h^3)/900
then i said that dV/dh = (pi h^2)/ 300
also dV/dt= dV/dh times dh/dt and i got dV/dt = (pi h^2)/ 750
then just to check i used subed in h = 30r in the volume formula and did all the same steps and got a different answer... so i kno im doing something wrong.. :S
can u please help me out here? i feel realli stupid