Math CentralQuandaries & Queries


Question from AMie, a student:

a small city produces 500,000 cubic ft of garbage per week. If all of this garbage were stacked neatly (in a nice vertical pile) on a 100-yard by 60-yard football field, how high would the pile be (in feet)?


There are 3 feet in a yard so the field is 300 feet by 180 feet.

Suppose the garbage were packed in boxes that are 1 foot by 1 foot by 1 foot, that is cubes that are 1 cubic foot in volume. You can place 300 of these boxes along the long side of the football field. Beside this row you can place another 300 boxes and so on until you have 180 rows of 300 boxes each to cover the entire football field. This would take 300 × 180 = 54,000 boxes or 54,000 cubic feet to cover the football field 1 foot deep in garbage.

A second one foot layer on top of this would take another 54,000 cubic feet of garbage.

How many layers would it take to use up all 500,000 cubic feet of garbage? This probably won't give in integer number of layers but you can spread out the top layer to make it a neatly stacked pile. How high is the pile?

I hope this helps,

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