I want a 3D Model of the Bitcoin logo with an exact volume. How to calculate?

[youdantoom]

If i take the Bitcoin logo and turn it into a 3D Model with the only requirement that it needs to be 56.753096768 cm³ (cubic centimeters) - what's my way of calculating the dimension of it?


The depth is unknown and determines the widht/height of the object but i can't find a way to figure out at what sizes i would reach exact 56.75309 cm³.

does anybody know how i could calculate this?

[Hispo]

I have two ideas to solve this problem:

1) Take the bitcoin logo (2D) and divide it into simple shapes which areas can be calculated easily and added. This will provide an aproximation of the area, then all you have to do is calculate the depth for your fixed volume.

Volume = Area * Depth


This can also be made using calculus, but it is way harder, because one would need to find functions which would draw the logo together, however the result would be exact.

2)You can 3D print a sample of known depth (10 cm, for example), once you have printed it, you find the volume by completely sumering it in a contained with a scale on volume.

once you have the volume, you can find the Area of the BItcoin logo

Area = Volume / Depth

Now that you have the Area, you simple recalculate the Depth for your desired Volume:

Depth = Volume /Area

And done!

[youdantoom]

now you brought me to conclusion, i could try any 3D modeling program, extrude the 2D one into 3D and it will most likely tell me the volume. or even easier, i know the cm² from the shape.
thanks for inspiration :-)

[Hispo]

now you brought me to conclusion, i could try any 3D modeling program, extrude the 2D one into 3D and it will most likely tell me the volume. or even easier, i know the cm² from the shape.
thanks for inspiration :-)

The software will most likely tell you the total surface of the 3D prisma, which is it useless for your purpose.
However, if you get the volume you can easily calculate de area as I explained.

keep in mind, that this volume is the outside volume.
If you are trying to print a container with a BTC share, you need to calculate the volume of the walls and calculate de difference with the former.

[franky1]

bitcoin logo is a circle.. so pretty simple to find a volume of a cylinder

volume in excel spreadsheet
=PI()*[radius cell]^2*[height cell]

so if you know the diameter of the circle you want.. half it and thats your radius
then to find out the needed corresponding height
=56.75309/(PI()*[radius cell]^2)

..
here is some examples if you only want to input 3decimal radius and height  to get your 5 decimal volume
radius       height
2.141   3.941
2.147   3.919
2.551   2.776
4.140   1.054
4.643   0.838