# A wooden crate has a mass of 780g, a height of 6.4 cm, a width of 8.7 cm, and a length of 52cm. What is the density of the crate?

##### 1 Answer

#### Explanation:

As you know, density is defined as mass **per unit of volume**

#color(blue)("density" = "mass"/"unit of volume")#

This means that every time a problem asks you to calculate a substance's density, your goal will basically be to determine the mass of **one unit of volume** of that substance.

In your case, the dimensions of the wooden crate are given to you in *centimeters*, By the time you'll finish determining the volume of the crate, you'll end up with *cubic centimeters*.

This means that must determine the mass of

So, you can think of your wooden crate as being a **rectangular prism** that has

a height of#"6.4 cm"# a width of#"8.7 cm"# a length of#"52 cm"#

As you know, the volume of a rectangular prism is given by the formula

#color(blue)(V = l xx w xx h)" "# , where

Plug in your values to get

#V = "52 cm" xx "8.7 cm" xx "6.4 cm"#

#V = "2895.4 cm"^3#

Now, you know that this crate has a mass of

#1 color(red)(cancel(color(black)("cm"^3))) * "780 g"/(2895.4color(red)(cancel(color(black)("cm"^3)))) = "0.2694 g"#

This means that the density of the wooden crate will be

#rho = "0.2694 g"/"1 cm"^3 = color(green)("0.27 g/cm"^3)#

The answer is rounded to two sig figs.