Calculus
posted by sara on .
Calculate the height of a cylinder of maximum volume that can be cut from a cone of height 20 cm and base radius 80 cm ,
please help me

radius = r = 80  (80/20)h
r = 80  4 h
v = pi r^2 h
v = pi (804h)^2 h
dv/dh = 0 for max or min
0 = (804h)^2 + h (2)(804h)(4)
0 = 6400640h+16h^2  640h+32h^2
48h^2  1280 h + 6400 = 0
6 h^2  160 h + 800 = 0
3 h^2  80 h+ 400 = 0
(3 h  20 )(h  20 ) = 0
h = 30 (no good, minimum)
or
h = 20/3 approximately 7