Maxima & Minima

Question

What is the radius of a cylindrical soda can with volume of 512 cubic inches that will use the

minimum material?

Answer 1

The volume of the can is πr²h = 512.

h=512/πr²

The surface area of the can is 2πr² + 2πrh.

Substitute the expression for h into the surface area formula.

Differentiate the surface area expression with respect to r and set the derivative equal to 0.

Solve for r.

This value of r gives the minimum surface area, i.e. the minimum material.