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

Question

Philoid · Accepted Answer

Let r and h be the radius and height of the cylinder.

Given that, volume of cylinder = 128π cm³

We know that , V = πr²h

⇒ 128π = πr²h

⇒

Let S be the Surface area of cylinder.

S = 2πr² + 2πrh

⇒ S = 2π(r²+rh)

⇒

Now ,

⇒

⇒ r = 4

At r = 4,

Hence, for r = 4, surface area is minimum.

∴ dimensions of the can for minimum surface area is r = 4cm and