Math CentralQuandaries & Queries


Question from John:

I am working with concrete and need some assistance please. I am trying to figure out what the surface space is for a one cubic foot that is four inches thick?

Thanks for your help....

Hi John,

The volume of a solid of uniform thickness is (the surface area) × (the thickness). If the surface area is measured in square feet and the thickness in feet then the resulting volume will be in cubic feet. There are 12 inches in a foot so 4 inches is 4/12 = 1/3 feet. Your volume is 1 cubic feet so

(the surface area) × 1/3 = 1


the surface area = 3 square feet.

This might be a rectangle 1 foot by 3 feet, or perhaps 1/2 foot by 6 feet, or a circle with area 3 square feet, or some other shape. As long as the surface area is 3 square feet and the thickness is 4 inches the volume is 1 cubic foot.


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