A trough is to be made to the dimensions shown, 20 feet long with bottom plank 1 foot wide and side planks 1 foot wide. Cross sections perpendicular to the base of the trough are isosceles trapezoids with shorter base and both legs having a length of 1 foot. Only the angle [math]\theta[/math] can be varied (though use of the slider.) [br][br]What value of [math]\theta[/math] appears to maximize the volume of such a trough?

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]