Tank measurments to gallons ratio

[mikecc67548]

I wonder how many gallons an empty hexagon tank holds that measure 11 1/2 inches to a side and a height of 59.69 centimeters?

 

[redfishblewfish]

To calculate the volume of a hexagonal prism you multiply 3 x apothem length x side length x height. The apothem length is the perpendicular distance from the center of the hexagon to any of its sides. Assuming you used inches, the answer will be in cubic inches, which can easily be converted to gallons by multiplying by 0.00432900433.

 

[Gandolfe]

length x width x height = cubic inches/231...is even easier

 

[nanojg]

length x width x height = cubic inches/231...is even easier

That will not work, re-read post

 

[Gandolfe]

just use a 5 gallon bucket and count how many it takes to fill it...LOL by the way 59.69 cm is 23.5 inches, but I bet it's about 26 gallons

 

[mikecc67548]

found this

 

[redfishblewfish]

found this

Mike, since this site does not show the calculations they are using, I will go through the math to verify the number you get from the quoted site.

Since I don't have your tank here, I can determine the apothem by simply knowing that one of the sides is 11.5 inches. Knowing this, I can determine the apothem by multiplying (I'm not going to derive this, just believe me and Pythagoras): 0.5 X SqRt 3 x 11.5

This tells me you apothem is 10 inches.

Knowing this I can now calculate the volume using the formula I posted above for a Hexagonal Prism....

(3 x apothem length x side length x height)

And this gives me 8107 cubic inches, which calculates to a 35 gallon tank.

Hope I didn't put you to sleep or give you flashback nightmares from 10th grade geometry! Enjoy.

 

[Gandolfe]

guess I was off by a few gallons...lol