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.

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- Dec 2nd 2008, 04:13 AMJen1603Maxima/Minima
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.

- Dec 2nd 2008, 07:11 AMSoroban
Hello, Jen1603!

Quote:

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]: .