how many case loads of bottled water can this semi truckpractically haul?
A typical semi-trailer should not be expressed by 12.5x8x40because a typical semi-trailer is bound by dept. of Transportationregulations that say max height is 13ft 6in and max width is 8ft 6in. If there were 12.5 feet of usable height, the trailer deckwould have to be 12 inches high which would leave no room for thetires. The deck on a typical semi-trailer is actually about 4.5feet high which only leaves 9 feet of usable height. The averagewidth on the highway today is 8 feet 6 inches and the two mostcommon lengths used today is a 45 foot long trailer and a 53 footlong trailer.
Since we know that formula for the volume of a box is volume=length x width x height, we can now build our equation.
The volume of a 45 foot semi-trailer would be the product ofV=(45)(8.5)(9) and expressed in cubic feet, so (45)(8.5)(9)=3,442.5cubic feet of usable area.
The volume of a 53 foot semi-trailer would be the product ofV=(53)(8.5)(9) and expressed in cubic feet, so (53)(8.5)(9)=4,054.5cubic feet of usable area.
Now, the actual question was not the volume of a trailer but thenumber of cases of bottled water the truck can haul. The problem isthat we can't accurately figure this without the dimensions of thecases of bottled water that are being loaded; however, I can usethe measurements from a typical bottle of water to build anequation.
Using a 20 ounce bottle of Sam's Choice bottled water I foundthat the bottle is 7.687 inches tall and the circumference at thewidest section is 8.625 inches. Since the bottle does not havesmooth and flat surfaces, we will have to use the principles forstacking spheres and other irregular shaped geometric figures todetermine the number of bottles that we can stack in a single case,as well as the number of cases we can stack in the usable area ofour semi-trailer.
The principles for stacking spheres and other irregular shapedgeometric figures, in layman's terms, states that in order todetermine the volume needed to stack irregular shaped geometricfigures, we must first determine the volume of the smallestpossible regular shaped geometric figure in which the irregularshaped geometric figure could be completely contained. In thiscase, the closest geometric figure to our bottle would be acylinder, so we must determine the smallest possible cylinderneeded to completely encapsulate the irregular shaped bottle ofwater. We do this simply by measuring at the points of the bottlewith the greatest dimensions. When stacking irregular shapedgeometric figures, there will be a spaces between parts the objectsthat is not used.
We can determine that the area needed to stack our bottles willbe a length of 2.75 inches, a width of 2.75 inches and a height of7.687 inches. The Sam's Choice bottled water comes in a case with 6rows of bottles, each row containing 5 bottles of water for a totalof 30 bottles per case. To figure the length (l) of the case, wesimply multiple the length of the bottle by the number of rows(2.75inches x 6 rows), so (l)= 16.5 inches. To figure the width (w)of the case we multiply the width of a bottle by the number ofbottles per row, (2.75 inches x 5 bottles per row), so (w)= 13.75inches. The height of the case is simply the height of the bottles,so (h)= 7.687 inches. We are now ready to build our equation forthe volume of a case of Sam's Choice bottled water.
The formula for the volume (V) of a rectangle is: Volume= lengthx width x height and expressed in cubic inches, so V=(16.5)(13.75)(7.687) so the volume of a case of Sam's Choicebottled water is 1743.988 cubic inches or 1.0093 cubic feet
We can now take the volume of the trailer and divide it by thevolume of a case of bottled water to determine a maximum number ofcases that we can load onto our trailer.
The volume of a 45ft trailer is 3442.5 cubic feet and the volumeof the case of water is 1.0093 cubic feet, so: 3442.5 cubic feet/1.0093 cubic feet= 3,410.779 so we can fit a total of 3,410 casesof water onto a 45 ft trailer.
The volume of a 53ft trailer is 4054.5 cubic feet and the volumeof the case of water is 1.0093 cubic feet, so: 4054.5 cubic feet/1.0093 cubic feet= 4,017.14 so we can fit a total of 4,017 cases ofwater onto a 53ft trailer.
The problem with this is that along with the Dept. ofTransportation regulations on height and width, we are alsorestricted to a maximum Gross Vehicle Weight of 80,000 pounds. The30 count cases of bottled water each weigh 37.5 pounds. This meansif we load the maximum number of cases onto a 45 foot trailer, thecargo weight alone would be 127,875 pounds and if we were loading a53 foot trailer, our cargo weight would be 150,637 pounds. So weare not limited by volume, we are limited by weight.
Since this is the case, we need to determine the maximum numberof cases we can load, without exceeding the weightrestrictions.
The average semi-tractor with a typical dry van trailer weighsabout 30,000 pounds empty. The weight difference between a 53 footand a 45 foot is not significant enough to consider. With a 30,000empty weight we would only be able to load another 50,000 pounds ofcargo. at 37.5 pounds per case of bottled water, the maximum numberof cases of Sam's Choice bottled water is:
(80,000 lbs - 30,000 lbs)/(37.5 lbs)= 1,333.333. The maximumnumber of cases we can load is 1,333 cases.
