Gold has a density of 19.32 g/cm3. what is the volume of a sample of gold with a mass of 27.63 grams?

 The volume is:  " 1.430 cm³ " .

Explanation:  

Volume, " V  = ? ; (unknown, we need to solve for this).
Density,  "D  = 19.32 g / cm³ ; 
mass , "m" = 27.63 g ; 

The formula for density is:  

  D = m / V ;   Divide each side of the equation by:  "(1/m)" ;
                    to isolate " V" on one side of the equation; and to solve for "V" ; 

1/m)*D = (1/m) * (m / V) ;

    to get:   

       D/m = ; ↔  1 / V ;  Take the reciprocal of EACH SIDE; to isolate "V" on each side of the equation:    

      m / D = V/1 ↔ V = m / D ;

    V = m / D ; 

         Now, plug in our given values for mass, "m" ; and Density, D";              to solve for "Volume, V " ;

    V  =  m / D  =  (27.63 g)  ÷  (19.32 g / cm³)  ;                
 
                       =  (27.63 g) * (1 cm³ / 19.32 g) ;
 
                       =   (27.63 ÷ 19.32)  cm³  ;
  
                       =   1.4301242236024845 cm³ ;

                                              → Round to "4 significant figures" ; 
                       =   1.430 cm³ .

   The volume is:  " 1.430 cm³ " .