# Question #faa56

May 16, 2016

$\text{42.4 g}$

#### Explanation:

The idea here is that you can use a substance's density as a conversion factor to go from grams to volume and vice versa.

Simply put, if you know the density of a substance, you can use it to determine the volume of a given mass of said substance. Likewise, if you are given the volume of the substance, you can use its density to determine the mass of the sample.

You're dealing with a rectangular prism, which means that you can use its dimensions to find its volume

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} V = \text{length" xx "height" xx "width} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, you will have

$V = {\text{3.00 cm" xx "2.50 cm" xx "1.80 cm" = "13.5 cm}}^{3}$

So, this substance is said to have a density of ${\text{3.14 g cm}}^{- 3}$. This tells you that every ${\text{1 cm}}^{3}$ of this substance has a mass of $\text{3.14 g}$.

Use this as a conversion factor to get the mass that will occupy a volume of ${\text{13.5 cm}}^{3}$

$13.5 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{cm"^3))) * overbrace("3.14 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(purple)("the given density")) = color(green)(|bar(ul(color(white)(a/a)"42.4 g} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to three sig figs.