Question

Question #8ad0c

Answer 1

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 `"0.384 g cm"^(-3)`, which means that every `"1 cm"^3` of this substance has a mass of `"0.384 g"`.

`"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 `"1 cm"^3` of this substance is

`"1 kg = 2.20462 lbs"`

Now, you should already know that

`"1 kg" = 10^3` `"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)` `"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

`"1 ft = 0.3048 m"`

A more useful form will be

`"1 ft"^3 = "0.3048 m" * "0.3048 m" * "0.3048 m"`

`= "0.028317 m"^3`

As you know, you have

`"1 m" = 10^2` `"cm"`

This means that `"1 cm"^3` will be equivalent to

`"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"))))`

`= "1 m" * "1 m" * "1 m" * 10^(-6)`

`= 10^(-6)` `"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)` `"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 `"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.