Question

Of all the closed cylindrical cans (right circular), which enclose a given volume of 100 cm3, which has the minimum surface area?

Answer 1

Suppose r and h be the radius and height of the cylinder, respectively. Now,

Volume (V) of cylinder = πr2 h

⟹ 100 = πr2 h

⟹ h = 100/ πr2

The surface area ( *) of the cylinder = 2 πr2 + 2 πr h = 2 πr2 + 2 πr × 100/ πr2

• = 2πr2 + (200/r)

Differentiate, we get

So, dS/dr = 4πr - (200/r)

For maximum or minimum, we must have