To maximize the volume of a cuboid with a constraint total surface area, the length, width and the height of the cuboid must be the same, ie. it must be a cube.

Anyone have any idea about how to maximize a triangular base prism with a constraint total surface area? (Please include proving.)

And also, is "maximize the volume of a solid with a constraint total surface area" same as "minimize the total surface area of a solid with a constraint volume" ?

Thanks for giving some comment!! :)

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