Start by writing  as  and
     then as , and then put it over , 
     and we start with this:



     We treat a unit just as we would treat a number or
     letter in algebra which is multiplied by a number. So we 
     want to cancel away the three  factors and bring 
     in .  We know that .  So there are
     two possible unit multipliers which we can make with
     that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by  three times, one for
     each  factor.  

 

     and then the 's cancel, like this:

 



     Now we want to cancel away the three  factors
     and bring in .  We know that . 
     So there are two possible unit multipliers which we can 
     make with that.  We can make the unit multiplier 
     or the unit multiplier .  The question
     is which one do we make.  Since we have  in the
     numerator, we must use the unit multiplier which has
      in the denominator so the 's will cancel.
     So we multiply by  three times, one for
     each  factor.  

 

     Then the 's cancel:



     So all we have left is:



     Multiply all that out with a calculator,
     and replace the  by 



     or 279936 cubic inches.

     Edwin