# Question bec07

Nov 5, 2015

${\text{0.95 g/cm}}^{3}$

#### Explanation:

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

color(blue)("density" = "mass"/"volume")" "#, or $\text{ } \textcolor{b l u e}{\rho = \frac{m}{V}}$

In your case, you know that the mass of the leather belt if equal to $\text{130 g}$, but what about it's volume?

Well, your belt is actually a rectangular prism for which you know that

• its length is equal to $\text{98 cm}$
• its width is equal to $\text{3.5 cm}$
• its height is equal to $\text{0.4 cm}$

The volume of a rectangular prism can be calculated using the formula

$\textcolor{b l u e}{V = l \times g \times h}$

In your case, the volume of the belt will be equal to

$V = {\text{98 cm" xx "3.5 cm" xx "0.4 cm" = "137.2 cm}}^{3}$

Therefore, you can now say that its density is equal to

$\rho = {\text{130 g"/"137.2 cm"^2 = "0.9475 g/cm}}^{3}$

You should round this off to one sig fig, the number of sig figs you gave for the height of the belt, but I'll leave it rounded to two sig figs

$\rho = \textcolor{g r e e n}{{\text{0.95 g/cm}}^{3}}$