Calculating Tank Volume For Octagon Tank.

[rustage]

Hi.

I have recently acquired a tank which is 14" x 14" x 77" (tower). I am trying to figure out the volume in litres. I've used the volume calculator on this site and with the measurements to the water level, it is working out at 218 litres - however, the tank is octagonal and I'm struggling with the maths to get an exact figure.

Would any of you clever folks be able to help.

Many thanks in advance.

Chris

 

[fatheadminnow]

Give me the measurements for A, B and C.

From there I will be able to figure out the area of that triangle, using the law of Cosine, and then figure out the total volume of your tank.

TOP VIEW

I will be back on in an hour to figure it out for ya.

S=1/2(A+B+C)

Area = Square root of (S(S-A)(S-B)(S-C))

Thanks

-FHM

 

[Colin_T]

maybe post this in the scientific section of the forum. There are plenty of smarties in there that should be able to help you work out the volume

 

[nmonks]

Chris, the easiest thing is this: half empty the tank at the next water change. Then add up the buckets of water you add to fill it back up again. Any inaccuracies will be trivial in terms of dosing medications, fertilisers, etc.

The thing with octagonal and hexagonal tanks is to always remember their volume is misleading when it comes to calculating how many fish you can add. Octagonal and hexagonal tanks are invariably taller than broad, and that means they have a poor surface area to volume ratio. In other words, there's less area at the top of oxygen to get into the water than would be the case for a rectangular tank of equivalent volume. This means you can safely keep fewer fish in an octagonal and hexagonal tank compared to a rectangular tank of equivalent volume.

Always use the surface area rule when estimating stocking. For small fish (neons, guppies, etc.) an old rule is to allow 10 square inches (e.g., a strip one inch wide and ten inches across, not ten by ten inches) per inch of fish length. So a tank with a surface area of 200 square inches would hold 20 inch-long fish safely.

Calculating the area of a octagon and hexagon is easy enough, and the formulas should be on Wikipedia and the like.

Cheers, Neale

 

[rustage]

Give me the measurements for A, B and C.

From there I will be able to figure out the area of that triangle, using the law of Cosine, and then figure out the total volume of your tank.

A=6"
b=7.5"
c=7.5"

the water is filled to 68"

Very grateful for your help.

Chris

 

[fatheadminnow]

Using the law of Cosine you get a total volume of 184 liters.

Proof...lol.

-FHM

 

[rustage]

Using the law of Cosine you get a total volume of 184 liters.

Proof...lol.

-FHM

I'm very impressed. Thanks so much. I'm setting up my first tank and didnt really want to guess.
Have a great night.

Chris

 

[fatheadminnow]

Your welcome!

-FHM

 

[OldMan47]

Why not just use 1/2 BH, that is half the base times the height. The height in this case would be half the distance between the flat sides and the base is the length of a flat side. Get the answer, multiply by the number of sides, it will work for hexagon or octagon. Multiply that by the height of the tank. No cosines, no square roots, just simple arithmetic. The answer should be the same but I have no limit on which direction I lay my tape measure.

 

[fatheadminnow]

Why not just use 1/2 BH, that is half the base times the height. The height in this case would be half the distance between the flat sides and the base is the length of a flat side. Get the answer, multiply by the number of sides, it will work for hexagon or octagon. Multiply that by the height of the tank. No cosines, no square roots, just simple arithmetic. The answer should be the same but I have no limit on which direction I lay my tape measure.

1/2(b)(h) ONLY works if the triangle is a square triangle (has a 90 degree angle) however this triangle was an Oblique triangle, meaning the angles it had did were not 9o degrees, that is why your either need to use the law of Cosines, or the law Sines to solve for area.

But I see where you are coming with by splitting the triangle in half.

I just looked at the triangle as a whole and solved from there, less room for error = more accurate answer.

-FHM

 

[OldMan47]

Actually it works with any triangle but you can't use the length of the sides as the height, you use the distance to the vertex measured along a line perpendicular to the base. In this case we are dealing with isosceles triangles which are a very convenient shape to measure. Instead of measuring corner to corner to get the length you marked as B and C, you measure from flat to flat to derive the distance from A to the place where B and C join, which is the height.

 

[fatheadminnow]

Actually it works with any triangle but you can't use the length of the sides as the height, you use the distance to the vertex measured along a line perpendicular to the base. In this case we are dealing with isosceles triangles which are a very convenient shape to measure. Instead of measuring corner to corner to get the length you marked as B and C, you measure from flat to flat to derive the distance from A to the place where B and C join, which is the height.

Yes this is true, and would've worked in this situation, however, 1/2(b)h) would be VERY hard to incorporate in a triangle that is not an isosceles triangle.

If the two angels that are coming off of the base are different from one another (not in this case) than the two sides are going to be of different lengths, therefore incorporating 1/2(b)(h) would be very hard, and therefore one would have to use either the law of cosines or the law of sines to solve for area.

But yes, 1/2(b)(h) would of worked in this situation because this triangle is an isosceles triangle.

Its kind of cool what you learn in math class can be used in real life situations like this.

Especially if you are only given like one angle and two sides, then one would have to use the law of Sines, Area = 1/2(b)(a)SinC

-FHM

 

[OldMan47]

It happens I was a math major in school although I have gone other directions since then. That does not mean I don't like the simple, mathematicians call it elegant, solution to a problem.

 

[fatheadminnow]

It happens I was a math major in school although I have gone other directions since then. That does not mean I don't like the simple, mathematicians call it elegant, solution to a problem.

Yeah, I am going for my BS in Mechanical engineering, so I have taken plenty of math classes as well! lol

That is cool that you were a math major back in school!

-FHM