06-09 Trapezoidal gutter of greatest capacity

Problem 06
A trapezoidal gutter is to be made, from a strip of metal 22 inches wide by bending up the edges. If the base is 14 inches wide, what width across the top gives the greatest carrying capacity.
 

Problem 07
Solve Problem 06, if the strip is 13 inches wide and the base width 7 inches.
 

Problem 08
Solve Problem 06 if the strip is 9 inches wide and the base width 3 inches.
 

Problem 09
Solve Problem 06, if the strip width is w and the base width b.
 

28 Review Problem - Amount of metal sheet used to construct a water tank

Problem 28
028-water-tank.gifA water tank, open at the top, consists of a right circular cylinder and a right circular cone, as shown. If the altitude of the cylinder is three times its radius, and the altitude of the cone is two times the same radius, find the number of square feet of sheet metal required to construct a tank having a capacity of 10,000 gal. (One gal. = 231 cu. in.)