Question

Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimeters, find the dimensions of the can which has the minimum surface area?

Answer 1

Let r and h be the radius and height of the cylinder respectively.
Then, volume (V) of the cylinder is given by,

∴By second derivative test, the surface area is the minimum when the radius of the

Hence, the required dimensions of the can which has the minimum surface area is given