Question

Of all the closed right circular cylindrical cans of volume 128π cm³, find the dimensions of the can which has minimum surface area.

Answer 1

Let r, h be radius and height of closed right circular cylinder having volume 128π cm³. 

If S be the surface area then

For extreme value of S,

Again,

Hence, for r = 4 cm, S(surface area) is minimum.

Therefore, 

Dimensions for minimum surface area of cylindrical can are radius r = 4 cm and h = \(\frac{128}{r^2}\) = \(\frac{128}{16}\) = 8 cm.