Expert: Vishwas K Hajirnis - 3/29/2004

Question
Hello I have just aquired an odd shaped fish tank, I would like to know how to calculate the volume of water it holds. The six sides are not all the same size so I am having trouble getting the formule correct. Please help.

Answer
I assume the tank is regular prism with hexagonal base.
( i.e. the sides (walls) of the tank are all vertical and the bottom cross section is identical to the top. In this case the volume of the tank will be area of the base multiplied by its height.
So the problem now reduces to finding the area of the base.

Now see whether you can simplify this further by dividing the given area into a number of triangles. For example by joining the vertices to one of the internal points you will be able to divide the base area into 6 triangles.
Now you may measure the sides of these triangles and calculate their areas and then later add up these areas.

Note that if you know all the sides of a triangles then you
can find its area by applying Hero's formula. viz. If
a triangle has sides equal to say a, b, & c. Then
let s be equal to (a+b+c)/2, and the area of the triangle
is given by
   (s*(s-a)*(s-b)(s-c))^(1/2)

   '*' denotes multiplication and ^ denotes exponentiation,
   Or the same formula in words will be =
   square root of ( s multiplied by (s-a) multiplied by (s-b)
   multiplied by (s-c))

For odd shaped areas one can also copy the shape on a graph
paper and add the no. of squares to get the area approximately.

Finally: Of course the volume can alternatively be measured
by simply measuring the total quantity of water it holds.
In fact in many industrial applications this is the standard
method of measuring the volume of odd shaped vessels.