A can of beans has internal radius r and height h. Given that Surface area is S = 2 pi r ( r + h ) and this is equal to 120 pi. Determine r and h such that the volume of beans in the can is a maximum.
We are given: . .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: . .
Substitute  into : .
Differentiate and equate to zero: .
. . and we have: .
Substitute into : .