Question

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?

Answer 1

Answer:  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 " .
______________________________________________