# Question 8ad0c

Jun 28, 2017

Here's how you can do that.

#### Explanation:

As you know, density represents mass per unit of volume.

In your case, an unknown substance is said to have a density of ${\text{0.384 g cm}}^{- 3}$, which means that every ${\text{1 cm}}^{3}$ of this substance has a mass of $\text{0.384 g}$.

${\text{density" = "0.384 g"/"1 cm}}^{3}$

Now, your goal here is to convert the mass from grams to pounds and the unit of volume from cubic centimeters to cubic feet.

A well-known conversion factor that you can use to convert the mass of ${\text{1 cm}}^{3}$ of this substance is

$\text{1 kg = 2.20462 lbs}$

Now, you should already know that

$\text{1 kg} = {10}^{3}$ $\text{g}$

so you can say that you have

0.384 color(red)(cancel(color(black)("g"))) * (1 color(red)(cancel(color(black)("kg"))))/(10^3color(red)(cancel(color(black)("g")))) * "2.20462 lbs"/(1color(red)(cancel(color(black)("kg")))) = 8.467 * 10^(-4) $\text{lbs}$

At this point, you can rewrite the density as

"density" = (8.467 * 10^(-4)color(white)(.)"lbs")/"1 cm"^3 color(white)(color(blue)( larr " equal to 0.384 g")/a

Finally, to convert the volume, use the conversion factor

$\text{1 ft = 0.3048 m}$

A more useful form will be

$\text{1 ft"^3 = "0.3048 m" * "0.3048 m" * "0.3048 m}$

$= {\text{0.028317 m}}^{3}$

As you know, you have

$\text{1 m} = {10}^{2}$ $\text{cm}$

This means that ${\text{1 cm}}^{3}$ will be equivalent to

$\text{1 cm"^3 = "1 cm" * "1 cm" * "1 cm}$

 = 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm")))) * 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm")))) * 1 color(red)(cancel(color(black)("cm"))) * "1 m"/(10^2color(red)(cancel(color(black)("cm"))))

$= \text{1 m" * "1 m" * "1 m} \cdot {10}^{- 6}$

$= {10}^{- 6}$ ${\text{m}}^{3}$

You can thus say that you have

10^(-6) color(red)(cancel(color(black)("m"^3))) * "1 ft"^3/(0.028317color(red)(cancel(color(black)("m"^3)))) = 3.5314 * 10^(-5) ${\text{ft}}^{3}$

At this point, the density of the substance is equal to

"density" = (8.467 * 10^(-4)color(white)(.)"lbs")/(3.5314 * 10^(-5)color(white)(.)"ft"^3) color(white)(color(blue)( larr " equal to 0.384 g")/color(blue)(larr " equal to 1 cm"^3)

To find the mass of one unit of volume, i.e. of ${\text{1 ft}}^{3}$, simply divide the numerator and the denominator

"density" = color(darkgreen)(ul(color(black)(24.0 color(white)(.)"lbs ft"^(-3))))#

The answer must be rounded to three sig figs, the number of sig figs you have for the density of the substance.