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