what measurement do you use to find out how many gallons are in a hexagon aquarium?

Question

I would like to find out how to measure how many gallons my aquiarium is18 inches deep and each side is of the hexagon is 24 inches long.

Answer 1

First find the area of the hexagon and multiply it by depth then convert cubed inches to gallons:
(3*squareroot of 3)/2 * lenght^2 or about 2.598 * L^2
1716.48 in squared * 18 in =
26936.064 cubed inches = 116.6 gallons

Answer 2

A regular hexagonal prism can be split into six triangular prisms with a cross section of an equilateral triangle (since 360/6=60).

By Pythagoras' Theorem, the height of these triangles = sqrt(24^2-12^2)=sqrt432=12sqrt3

The are of the triangle = 24*12sqrt3/2=144sqrt3

The hexagon= 6*144sqrt3=864sqrt3

The whole prism = 18*864sqrt3=15552sqrt3 is roughly equal to 26936.85 inches^3 (To 2 dp)

1 inch^3=0.00432900432900433gallons so 26936.85 inches^3= (ans) 116.61 gallons (to 2 dp)

Sorry, I previously forgot to convert into gallons.

Please pick me for best answer!!!

Answer 3

116.60975827 gallons.
It's pretty complicated but that's your answer.