Relative Length to Relative Volume

[Aureum]

I understand relative length well but I what to image a 3d object traveling close to the speed of light. As we know objects have speed, direction, and rotation. So I was wondering if there is a general equation to calculate the relative volume change of a Rectangular Prism rotating and traveling near the speed of light at any given time.

Relevant equations

 

[bcrowell]

When you say you want to "image" the object, do you mean that you're actually trying to draw a picture of what it would look like optically? If so, then you can't just do that using the Lorentz contraction, because you also get effects from the time it takes light rays to reach your eye.

If all you mean is that you want to calculate the volume as expressed in a frame where the object isn't at rest, then the volume is reduced by the same factor as the length. There is no Lorentz contractions along the two transverse axes.