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Reply.
Hello Karen. Lets calculate the volume of your aquarium,
which has a hexagon for the base and a height of
24.75". Click
here to see a picture of a hex-aquarium.
The formula for volume
is always the base times the height, which you measured
24.75". So all we need is the area of the base.
Since all 6 panels
in your aquarium are 12", the base is a so-called
regular hexagon with all the sides measuring 12".
The area of this regular hexagon is 6 times the
area of an equilateral triangle with each side 12".
Now think of a 12"
equilateral triangle, and divide into two right
triangles with one side 6" and hypotenuse
12". The other side will have a length equal to
the square root of 12x12 - 6x6, which equals the
square root of 144 - 36, which is the square root
of 108, or about 10.4".
The area of the right
triangle is 1/2 x 6 x 10.4, and the area of the
equilateral triangle will be twice as much, which
is 6 x 10.4 = 62.4 square inches, so the area of
the base of your aquarium is 6 x 62.4, or 374.4
square inches.
The volume of your
aquarium is the area of the base times the height
= 374.4 x 24.75 = 9296.4 cubic inches. Now
multiply by 0.00433 to convert cubic inches to gallons:
9296.4 x 0.00433
= 40.1 gallons, which answers your question.
When you calculate
something like this, and the answer is important,
because you may use the answer to determine how
much Quick Cure or Salt to add to your aquarium,
then it's best to double check your calculation.
Or you might end up forgetting that the equilateral
triangle has two right triangles, and get an answer
that is off by a factor of 2.
Here is one way to
double check the answer. The hexagonal base of your
aquarium could fit inside a circle with a radius
of 12" and have an area of about
pi x 12 x 12 = 3.14
x 12 x 12 = 452.2 square inches
which is somewhat
bigger than the 374.4 square inches for the area
of the hexagon inside the circle. So that checks.
A circle with a radium
10.4" would fit inside the hexagon, and that circle
would enclose an area of about
pi x 10.4 x 10.4
= 3.14 x 10.4 x 10.4 = 327.8 square inches
which is less than
the 374.4 square inches for the area of the hexagon.
So that checks too.
Also the area of
the hexagon should be about half-way between the
area of the inner circle and the area of the outer
circle. The areas are about 327.8, 374.4, and 452.2,
so those numbers look about right.
Now lets check these
calculations with a measurement. Your aquarium is
24.75" tall. When you change 20% of water, as recommended
repeatedly in this web site, you should remove 20%
x 24.75 = 4.95, or about 5" of water. So measure
down from the water surface 5" and put a mark on
the glass with a marker pen.
Now remove water
down to the mark and keep track of how much water
you remove. For example, you could use a clean one-pint
measuring cup. You should get close to 64 pints,
which is the same as 8 gallons, or 20% of the 40
gallons, that we calculated in your aquarium. (Be
sure to thoroughly clean the measuring cup, when
you finish using it.)
You will probably
measure less than 64 pints. Maybe you'll get 61.
Because the measurements for your aquarium that
you gave in your email were probably the outside
measurements, and the water fills the inside of
your aquarium.
You could improve
the calculations above by doing them again with
the inside measurements, and perhaps subtracting
the volume of the ornaments, etc. Click
here for more about doing that.
I hope this has thoroughly
answered your question.
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