Alright, I had too much time on my hands and worked through some examples here…
In the case of 6.5x5 (assuming 6.5 is length and 5 is circumference (aka girth))…
(Circumference / pi = Diameter)
5 / pi = 1.592
(Diameter / 2 = Radius)
1.59 / 2 = 0.796
(Estimated Volume = pi * Radius squared * Length)
pi * (0.796)^2 * 6.5 = 12.931 in^3
To double your volume, and assuming equal amounts of length and girth gain, you would do the following…
Double volume = 12.931 * 2 = 25.863 in^3
Now, I did a lot of algebra and had to solve a cubic equation, and got this…
New Length = 6.410 in
New Girth = 7.910 in
(For reference, my original cubic equation was as follows…
pi * [(5 + x) / (2 * pi)]^2 * (6.5 + x) = 25.863
which then reduces to…
x^3 + 16.5x^2 + 90x - 162.5 = 0
This gives a real solution of x = 1.410, or complex conjugate solutions of -8.955 + 5.921i and -8.955 - 5.921i, but since none of us have imaginary dicks, those two complex conjugate answers don’t apply, hence x = 1.140.
So, to get new length and girth, merely add 1.140 to the length and girths of 6.5 in and 5 in, respectively.)
However, if you wanted to grow in proportion to the current length and girth and wanted to double your volume, the following calculation is needed…
The current ratio of length to girth is 6.5 / 5 = 1.3
So after some drawn out algebra and solving for the only real solution to the cubic equation, you get the following…
New Length = 8.189 in
New Girth = 6.300 in
(For reference, my original cubic equation was as follows…
pi * [(5 + x) / (2 * pi)]^2 * (6.5 + 1.3x) = 25.863
which then reduces to…
1.3x^3 + 19.5x^2 + 97.5x - 162.5 = 0
This gives a real solution of x = 1.300, or complex conjugate solutions of -8.150 + 5.456i and -8.150 - 5.456i, but since none of us have imaginary dicks, those two complex conjugate answers don’t apply, hence x = 1.300.
So, to get new length and girth, merely add 1.300 to the girth and 1.689 (1.3 *1.300 = 1.689) to the length.)
Alright, I went kinda crazy with answering this question, but I figured I’d put my electrical engineering degree and my math minor to some use, hehe.
The best way to find volume however, would probably be the water displacement method as mentioned above. However, the volume estimation method is good as the estimate it is.