Hi Karlos,

The volume of the trough can be subdivided into the central cube

and the two outside pyramids.

To calculate volume, use

hence you must express the trough's height "h" in terms of

The cross-sectional area of the right and left triangles are

Hence the volume of the trough is

Theta giving max volume is found by differentiating this and setting it to zero, using the product rule of differentiation

For an acute angle use the first factor