A trapezoidal trough is to be made from a strip of tin 20 inches wide by bending up the edges. If the base is 8 inches, find the dimensions and the area of the trough of maximum capacity made in.

Question

Please include your solution on how you answer the problem. Thank you!

Answer 1

i assume the ends are left open?

max capacity = max volume = max cross sectional area since this is a prism.

so trapezoidal cross sectional area is (8+x)/2 * ((x-8)/(tan(arcsin((x-8)/12)))), x are the sloped sides.

differentiate to find the peak