Question

Cans of soups are 12 fl oz and are 4.3 in tall. These cans are shipped to stores in packs that are 2 cans high, by 4 cans wide, and 5 cans deep. The store pays the shipping company $100 dollars per cubic meter. How much does one pack of soup cost to ship? How much does the company pay to ship the empty spaces between the cans in one pack?

Answer 1

1 fl oz = 2.9574 X 10^-5 metre³

Thus 12 fl oz = 0.000354882 metre³

1 inch = 0.0254 metre

thus 4.3 inch = 0.10922 metre.

The cans should thus have base area of 12 fl oz/4.3 inches

If R is the radius of the base of can then

Thus

or the diameter

Volume of each pack = (height of one can x 2)(diameter of one container x 4)(diameter of one container x 5)

Total cans in a pack = 2 x 4 x 5 = 40 cans/pack.

Cost of shipping 1 cubic meter = 100$

thus cost of shipping one pack = 100 x 0.01807 = 1.807$

Thus cost of shipping one can = 1.807/40 = 0.045175 dollars/can.

Empty space in one pack = length x breadth x height - 40 x volume of one soup can

Empty Space =

Thus price paid for empty space = 100 x Empty space = 100 x 0.0038747 = 0.3874 dollars/pack.