Determine the height and radius of cylinder of volume 512 cm3 which has the least total surface area

Answer 1

πr^2h = 512
So, h = 512/(πr^2)

area a = 2πr^2 + 2πrh
= 2πr^2 + 2πr (512)/(πr^2)
= 2πr^2 + 1024/r

Assuming you have calculus, we see that

da/dr = 4πr - 1024/r^2
da/dr=0 when r = 4∛(4/π)

Now you can find h.