Of all the closed cylindrical cans (right circular), which enclose a given volume of 100 cm3, which has the minimum surface area?
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
>0
This is the condition for minima
From equation 1,
Hence, required dimensions of cylinders are radius = and height =