What Is The Volume Of A Hexagonal Fish Tank That Is 30" High And Is 14" Long On Each Side And 28" Across From One Corner To Opposite Corner?


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We know each angle is 180 degrees divided by 6 since it has 6 sides.  That makes each angle 30 degrees.  Let's cut off the four triangular sides to make it a rectangle, then add them back in.
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Then by trig, we can find the distance each left and right vertex jut out from the rectangular part of the tank.

sin(30) = opp/hyp.    and you said the faces are 14 inches.  so the opposite side of each triangle is sin(30) * 14 inches, or 7 inches.

because(30) = adj/hyp.  so the adjacent leg of each triangle is 0.866 * 14, or 12.1 inches.  So your tank should be 24.2 inches from flat side to the opposite flat side.

Now if we rearrange the triangles from one side to fit next to the other side, we can make another rectangle 7 inches by 24.2 inches.
And that sits next to the rectangular part of the tank which is 14 inches by 24.2 inches.

So a hexagonal tank is 1.5 times the volume of one made from just the center rectangular section.

Cross section is (7 + 14) * 24.2 inches^2  which is equal to 22 * 24.2, or 508.2 square inches.
The volume is the cross section multiplied by the height, or 508.2 x 30, which equals 15246 CUBIC inches.

There's 231 cubic inches per gallon, so that's 66 gallons.  Filled to the brim.  A pretty good sized tank.  Call it 60 gallons so you don't spill over the top!

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