Question

What is the density of an object with a mass of 24 grams and volume of 30 cubic centimeters?

Answer 1

Answer:  The density is: "0.8 g per cubic centimeter" ;

                  or:  write as "0.8 g per cm³ ."

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Explanation:

Note that:

 " $D=m/V$ " ;

that is:  Density = mass $per$ unit volume;

          The equation is "mass divided by Volume".

Since even in equation form; the equation is "mass per [unit] volume" ;

 We can solve this problem as a "unit rate problem"—albeit within

the conventional standard "units" used as appropriately and customarily.

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So:  Using this equation—Solve for:  " ____" :

  →  $D=m/V$

in which:

      D refers to:  Density ;  for which we shall solve.

      m refers to:  mass ;

[Note:  By convention; in units of "grams" [or;  "g"] } ;

     "V" refers to "Volume";
[Note: By convention;  in single "stand-alone units."].
      of:  "mL" [milliliters] ; or:  "cubic centimeters" [cm³ ] ;
 →  Note that usually, "mL" is the most commonly used "unit" for measuring liquids/solvents—and that "cm³ "; that is: "cubic centimeters"
—is the most commonly used "unit" for measuring the volume of solids—such as within this very question.}.

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So, we are given:  " m = 24 g ";  and:  " V = 30 cubic centimeters" ;

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Plug this into the equation for "Density; "D" ;  and solve:
$D = \frac{m}{V} = \frac{24g}{30CubicCentimeters} =\frac{24}{30}$$D = \frac{m}{V} = \frac{24g}{30CubicCentimeters} =(\frac{24}{30}) \frac{g}{CubicCentimeter}$;
                                      ↔       $\frac{24}{30}=\frac{(24/6)}{(30/6)}=\frac{4}{5}$ ;
Let us convert our fraction to a decimal form;  since a density value of a fraction is awkward.
      →  $\frac{4}{5} = \frac{?}{10}$ ;

  To find the "?" value, here is the explanation:  We use the value of "10" as the denominator to help convert this value to "decimal form".

Cross-factor multiply.
 That is:  Given:

      $\frac{a}{b} = \frac{c}{d}$ ;  $b\neq 0$ ;  $d$ $\neq 0$ ;

    ⇒  " $ad = bc$ "  ;

Thus:  10(4) = 5(?) ;  
 →  40 = 5*(?) ;   Now: divide each side by "5" ; to solve for: "?"

 40/5 = 5(?) / 5 ;

→  "?" = 8 ;

So: "4/5" = "8/10" ; that is:  "(8÷10)" = 8. ÷ 10 = 0.8

  The density; D of the object [described in the question]:

             is:  "0.8 g per cubic centimeter" ;

            or:  write as:  "0.8 g per cm³ " .
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Hope this is helpful to you. Best wishes!