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Old 04-25-2016, 04:00 AM   #1
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calculating home made octagon tank

I have recently been given this very odd long octagon tank that I aim to turn into an indoor aquaponics system. The trouble is that the man who made it so many years back for my mother-in-law has since passed away and she has no idea the gallons of the tank. Now, I remember basic math and volumes and with the help of some online tutors and some google unit conversions I calculated that the tank is 121 gallons. But that just doesn't seem right. It appears closer to a 50-70 gallon tank in my opinion. Does anyone have any advice on figuring the volume of an octagon tank that doesn't have equal sides? I would greatly appreciate any advice. The measurements are in inches. I apologize for not having a photo of the tank itself but I have not relocated the tank to my home yet.
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Old 04-25-2016, 10:18 AM   #2
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I confess I can't calculate in inches.

Can you break the shape up into smaller rectangles and triangles and work out those? Then add volumes together.
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Old 04-25-2016, 02:07 PM   #3
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Thank you for your reply. I attached a photo to the thread that shows that's what I've done. I broke it down to 3 rectangles and 4 triangles and calculated them individually and somehow got 121 gallons but It's just hard to believe honestly. The tank really isn't that big. I'm afraid that if my tank needs any kind of treatment to be added based on the number of gallons I won't be able to accurately treat it and I don't want to harm my fish.
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Old 04-25-2016, 03:39 PM   #4
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I think you've got the right idea. But your diagram seems to be missing at least one if not more measurements to confirm. Backwards engineering your math and I'm coming up with a tank height of 20 inches? Assuming your measurements are in inches anyway?

Also not sure if the photo is to scale? If I'm seeing it correctly you've got "11" next to each of the three sides of the triangles? The diagram does not look like equilateral triangles.

I see the long side of each rectangle is 40 but what is the short side? is it 11? If so then each of the rectangles would be about 38 gallons each; plus the long rectangle in the middle and each of the triangles on the end.

If all else fails you can start filling one gallon at a time to confirm!
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Old 04-25-2016, 04:10 PM   #5
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I think you've got the right idea. But your diagram seems to be missing at least one if not more measurements to confirm. Backwards engineering your math and I'm coming up with a tank height of 20 inches? Assuming your measurements are in inches anyway?

Also not sure if the photo is to scale? If I'm seeing it correctly you've got "11" next to each of the three sides of the triangles? The diagram does not look like equilateral triangles.

I see the long side of each rectangle is 40 but what is the short side? is it 11? If so then each of the rectangles would be about 38 gallons each; plus the long rectangle in the middle and each of the triangles on the end.

If all else fails you can start filling one gallon at a time to confirm!

Correct! It is to scale and the measurements are inches. The height is roughly 20" (I'll know for sure when I remove the wooden tank cap). I have gone over it so many times, the triangles are in fact equilateral at 11". The center rectangle is 5x62 and the other two are 11x40. I racking my brains on how this tank could hold so much when a rectangular tank nearly twice its size is 100 gallons. I guess I'll have to go old fashioned and spend my day filling it one 5 gallon bucket at a time. Ugh. Thanks for all your help, friends!
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Old 04-25-2016, 04:45 PM   #6
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Correct! It is to scale and the measurements are inches. The height is roughly 20" (I'll know for sure when I remove the wooden tank cap). I have gone over it so many times, the triangles are in fact equilateral at 11". The center rectangle is 5x62 and the other two are 11x40. I racking my brains on how this tank could hold so much when a rectangular tank nearly twice its size is 100 gallons. I guess I'll have to go old fashioned and spend my day filling it one 5 gallon bucket at a time. Ugh. Thanks for all your help, friends!

Double check your measurements as something doesn't sit right with me....especially at the triangles. That outside edge can not be the same as the other 2 edges if there is truly a right angle as it appears on your diagram.
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Old 04-25-2016, 05:06 PM   #7
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You're right. But finding the area of a right triangle only requires the length of the 2 sides that make the right angle. The hypotenuse is actually 15.6 (roughly). But I only need the 2 11's to find the area.
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Old 04-25-2016, 07:38 PM   #8
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For picture in your head. Move the two triangles on the left over to the right, and for the moment forget about the extra 5x11 between the left triangles, you now have a square surface area of 40"+11" (55) x 11"+11+5 (27) 55length, x 27 depth by 20 height. This is much bigger than any 55 or 70 gallon tank i'm aware of, and you still have a 5"x11"x20" *piece* I didn't include (cuz it mess' up my pretty square box for imagery. )

*disclaimer, I am no Math teacher, but I did stay at a Holiday inn.


-edit, see messed up simple addition! ha!
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Old 04-25-2016, 09:47 PM   #9
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For picture in your head. Move the two triangles on the left over to the right, and for the moment forget about the extra 5x11 between the left triangles, you now have a square surface area of 40"+11" (55) x 11"+11+5 (27) 55length, x 27 depth by 20 height. This is much bigger than any 55 or 70 gallon tank i'm aware of, and you still have a 5"x11"x20" *piece* I didn't include (cuz it mess' up my pretty square box for imagery. )

*disclaimer, I am no Math teacher, but I did stay at a Holiday inn.


-edit, see messed up simple addition! ha!

I think if this many people have looked at my math and measurements and we're all coming up with the same thing then it must actually be much bigger than it appears to me. Thank you all for your help! I'll take this thread down as soon as I figure it out.
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Old 04-26-2016, 12:34 AM   #10
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if the center "rectangle" is 40" x 27" x 20" =21,600 / 231 = 93.5 gallons
then if we take the two ends, join them into a hexagon, then we convert the side dimensions; (54" total / 6 sides = 9" side) and assuming 20" height, we get a volume of 21 gallons.
so the total volume is ~114.5 gallons.

at least that is what my addled mind came up with.


Here is a nifty tool for this, but limited in shapes;
Aquarium Volume Calculator
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