Hello, Jen1603!

We are given: . .[1]A can of beans has internal radius and height

Given that surface area is and this is equal to ,

determine and such that the volume of the can is a maximum.

The volume of a cylindrical can is: . .[2]

Substitute [1] into [2]: .

Differentiate and equate to zero: .

. . and we have: .

Substitute into [1]: .