# Question dd9db

Aug 11, 2015

Mass: 306 g

#### Explanation:

Density is defined as mass per unit of volume, which means that in order to calculate mass from an object's density you first need to determine its volume.

$\text{density} = \rho = \frac{m}{V}$

Notice that the object's density is given in grams per cubic centimeter, but that its dimensions are given in milimeters.

In order to get the units to match, you need to calculate the volume and then convert it from cubic milimeters to cubic centimeters.

You're dealing with a rectangular prism, which means that its volume will be

$V = l \cdot w \cdot h$, where

$l$ - its length;
$w$ - its width;
$h$ - its height.

In your case, you have

$V = {\text{20.0 mm" * "30.0 mm" * "45.0 mm" = "27,000 mm}}^{3}$

Convert this value to cubic centimeters

27,000color(red)(cancel(color(black)("mm"^3))) * "1 cm"^3/(1000color(red)(cancel(color(black)("mm"^3)))) = "27 cm"""^3

Since you know that the object's density is ${\text{11.34 g/cm}}^{3}$, and that you're dealing with ${\text{27 cm}}^{3}$, you can calculate its mass to be

27color(red)(cancel(color(black)("cm"^3))) * "11.34 g"/(1color(red)(cancel(color(black)("cm"^3)))) = "306.18 g"#

Rounded to three sig figs, the number of sig figs you gave for the dimensions of the rectangle, the answer will be

$m = \textcolor{g r e e n}{\text{306 g}}$