06-09 Trapezoidal gutter of greatest capacity Jhun Vert Fri, 05/08/2020 - 03:14 pm

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.
 

41 - 42 Maxima and Minima Problems Involving Trapezoidal Gutter Jhun Vert Wed, 05/06/2020 - 11:40 am

Problem 41
In Problem 39, if the strip is L in. wide, and the width across the top is T in. (T < L), what base width gives the maximum capacity?
 

Problem 42
From a strip of tin 14 inches a trapezoidal gutter is to be made by bending up the sides at an angle of 45°. Find the width of the base for greatest carrying capacity.
 

38 - 40 Solved problems in maxima and minima

Problem 38
A cylindrical glass jar has a plastic top. If the plastic is half as expensive as glass, per unit area, find the most economical proportion of the jar.
 

Problem 39
039-figure-39.jpgA trapezoidal gutter is to be made from a strip of tin by bending up the edges. If the cross-section has the form shown in Fig. 38, what width across the top gives maximum carrying capacity?
 

Problem 40
Solve Ex. 39, if the strip is 11 inches wide and the base is 7 inches wide.