Math CentralQuandaries & Queries


Question from Frank, a parent:

how many gallons of water in an 8" hexagon shaped box. 6" sides x 12.5" high? The walls are 1" thick , beveled @ 30 degrees, so inside dimensions are 6"

Hi Frank,

The volume of a prism is the area of the base times height. The hexagon you describe is regular with side length 6 inches so you can find its area in square inches using Stephen's expression for the area of a regular polygon with n sides or a different technique he used for the area of a regular hexagon.

Once you have the volume in cubic inches, say $A$ cubic inches you can use Google to find the volume in gallons. Just type $A$ cubic inches in gallons into the Google search window.


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