Geometry pls help

 

I don't know if it's a coincidence,   

but if you mutiply those areas                        12 x 8 x 6 = 576   

 

then take the sqrt of the product                    sqrt(576) = 24    

 

that's the same as the volume.  

_.

 

Oh, I see how it works now   

 

                                                      area₁  x  area₂  x  area₃     

 

                                                     (4 x 3)  x  (4 x 2)  x  (3 x 2)    

remove parentheses                      4 x 3   x   4 x 2   x   3 x 2      

rearrange and group                     (4 x 3 x 2)   x   (4 x 3 x 2)  

 

                                                                   24  x  24    

That's how it happens  

_.