# A sample of iron that has density of 7.833 g/mL has a mass of 94 g. If the sample is in the shape of a rectangular cube, what is the height of the cube if the top is 2 cm x 3 cm?

Aug 30, 2017

$\text{1 cm}$

#### Explanation:

You know that the sample is shaped as a rectangular cube, i.e. a rectangular prism, which means that you can determine its volume by using the equation

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{V = l \times w \times h}}}$

Here

• $l$ is the length of the rectangular prism
• $w$ is its width
• $h$ is its height

Now, you know that iron has a density of ${\text{7.833 g mL}}^{- 1}$. This means that every $\text{1 mL}$ of iron has a mass of $\text{7.833 g}$.

In your case, the sample has a mass of $\text{94 g}$, which means that it will occupy a volume of

94 color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(7.833 color(red)(cancel(color(black)("g")))))^(color(blue)("the density of iron")) = "12.0005 mL"

At this point, you should know that

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

so you can say that the volume of the prism is equal to

$V = {\text{12.0005 cm}}^{3}$

Since you know the volume of the prism, you can rearrange the equation to solve for its height

$V = l \cdot w \cdot h \implies h = \frac{V}{l \cdot w}$

Plug in your values to find

h = ("12.0005 cm"^color(red)(cancel(color(black)(3))))/(3 color(red)(cancel(color(black)("cm"))) * 2 color(red)(cancel(color(black)("cm")))) = color(darkgreen)(ul(color(black)("1 cm")))

The answer is rounded to one significant figure, the number of sig figs you have for the length and width of the prism.