how many cases of h20fit in a truck 45 ft.long8.5 ft.wide9 ft.tall

Question

The case of water is 10.2in.tall, 15.1 in.long, 8.3 in . wide. Truck trailer is 45 ft.long, 8.5 ft.wide and 9 ft.tall. how many bottles of water can be transported and how much extra space is there?

Answer 1

Dimensions of trailer in inches: 45' long=540in; 8.5' wide=102in; 9' tall=108in.
Volume=5,948,640 cu in.
Volume of case=10.2*15.1*8.3=1,278.366 cu in. Theoretical max no. of cases=4,653.
Packing arrangements: 10*10.2=102in=width of trailer.
7*15.1=105.7in. Height of trailer=108in.
65*8.3=539.5in. Length of trailer=540in.
Best fit of cases is 10*7*65=4,550.
Total volume of cases=4550*1278.366=5,816,565.3 cu in.
Unused space=5948640-5816565.3=132,074.7 cu in=76.43 cu ft approx. (1,728 cu in=1 cu ft)