math
posted by febie on .
A container in the shape of a right circular cylinder with no top has surface area 3*pi (m2). What height h and base radius r will maximize the volume of the cylinder ?

surface area = πr^2 + 2πrh = 3π
r^2 + 2rh = 3
h = (3  r^2)/(2r)
V = πr^2h = (πr/2)(3r^2)
= (3π/2)r  (π/2)r^3
dV/dr = 3π/2  (3/2)πr^2
= 0 for a max/min of V
(3π/2)r^2 = 3π/2
r^2 = 1
r = ± 1, but r > 0
r = 1
then h = (31)/2 = 1
check my arithmetic