determine the diameter of closed cylindrical tank in meters if the volume is 11.3m^3 to get min. surface area.

Answer 1

you know that

v = π r^2 h, so h = v/(πr^2)

the area is

a = 2πr(r+h) = 2πr(r + 11.3/(πr^2))
= 2πr^2 + 22.6/r

for minimum area, da/dr=0, so
da/dr = 4πr - 22.6/r^2
= (4πr^3-22.6)/r^2

da/dr=0 when 4r^3-22.6=0, or r=1.216

The diameter d = 2r.