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 Question from Carlene: I need to work out how many tyres will go in a shipping container. The shipping container is 10 foot long, 8 foot wide and 8.6 foot high. The tyre is 175 millimeters across and it is 14 inches in tyre thickness. How many tyres will fit in my container?

Hi Carlene.

If you think of "stacks" of tyres, then each has a width equal to length times a height, but there are three ways of orienting the stack to waste more or less space in the container.

I'd start by converting things to inches and cubic inches.

Watch how I solve the problem for my smaller "shipping container":

Question: Each bagel is 10 cm in diameter and 2 cm high. How many (at most) can you fit in a box that is 15 cm by 32 cm by 19 cm?

Solution:

1. If I stack the bagels along the 15 cm side, I can stack 7 bagels in that dimension (15 > 2cm x 7 bagels). I can only put 1 bagel in the 19cm dimension (19 > 10cm x 1 bagel) and 3 along the 32 cm dimension (32 > 10cm x 3 bagels). Thus I have 7 x 1 x 3 = 21 bagels.

2. If I stack them along the 32 cm side, I have 32 = 2cm x 16 bagels there, still 19 > 10cm x 1 bagel in the 19cm dimension and 15 > 10cm x 1 in the last dimension, so I only can put 16 bagels in it this way.

3. If I stack them along the 19 cm side, I have 9 bagels there and 1 bagel on the 15cm side and 3 on the 32 cm side, so that is 9 x 1 x 3 = 27 bagels. This is the best choice.

I guess my bagels are really skinny. Try it with your measurements for your tyres and container.

Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.