Q. 5 5.0( 2 Votes )

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

Answer :

Let the radius and height of right circular cylinder be r and h respectively.

Given: Volume of Cylindrical can = 100 cm3

Volume of a cylinder = πr2h

πr2h = 100

… 1

Surface of a cylinder, S = 2πrh + 2πr2

From equation we get,

Condition for maxima and minima

So, for


This is the condition for minima

From equation 1,

Hence, required dimensions of cylinders are radius = and height =

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