The density of brass is $8.89 {g/cm}^{3}$ $8.89" g/cm"^3$ . What is the density in kilograms per cubic meter?

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Answer 1 · 2018-03-23T18:56:16

$8890 {kg/m}^{3}$ $8890" kg/m"^3$

Begin the dimensional analysis by writing the given as a fraction:

$\frac{8.89 g}{{cm}^{3}}$ $(8.89" g")/"cm"^3$

Multiply by the conversion factor from grams to kilograms:

$\frac{8.89 g}{{cm}^{3}} \frac{1 kg}{1000 g}$ $(8.89" g")/"cm"^3(1" kg")/(1000" g")$

Multiply by the conversion factor from cubic centimeters to cubic meters:

$\frac{8.89 g}{{cm}^{3}} \frac{1 kg}{1000 g} \frac{{(100 cm)}^{3}}{{(1 m)}^{3}}$ $(8.89" g")/"cm"^3(1" kg")/(1000" g")(100" cm")^3/(1" m")^3$

Make sure that all of the units cancel, except ${kg/m}^{3}$ $" kg/m"^3$ :

$(8.89cancel" g")/cancel("cm"^3)(1" kg")/(1000cancel" g")(100cancel" cm")^cancel(3)/(1" m")^3= 8890" kg/m"^3$

The density of brass is 8.89" g/cm"^38.89 g/cm38.89" g/cm"^3. What is the density in kilograms per cubic meter?