# How are density mass and volume related?

Jan 11, 2014

They are related by the the density triangle.

#### Explanation:

They are related by the the density triangle. d = $\frac{m}{V}$

m = d×V

V = $\frac{m}{d}$

DENSITY

Density is defined as mass per unit volume.

d = $\frac{m}{V}$

Example:
A brick of salt measuring 10.0 cm x 10.0 cm x 2.00 cm has a mass of 433 g. What is its density?

Step 1: Calculate the volume
V = lwh = 10.0 cm × 10.0 cm × 2.00 cm = 200 cm³

Step 2: Calculate the density

d = $\frac{m}{V}$ = (433 g)/(200 cm³) = 2.16 g/cm³

MASS

d = $\frac{m}{V}$

We can rearrange this to get the expression for the mass.

m = d×V

Example:
If 500 mL of a liquid has a density of 1.11 g/mL, what is its mass?

m = d×V = 500 mL × $\frac{1.11 g}{1 m L}$ = 555 g

VOLUME

d = $\frac{m}{V}$

We can rearrange this to get the expression for the volume.

V = $\frac{m}{d}$

Example:
What is the volume of a bar of gold that has a mass of 14.83 kg. The density of gold is 19.32 g/cm³.

Step 1: Convert kilograms to grams.

14.83 kg × $\frac{1000 g}{1 k g}$ = 14 830 g

Step 2: Calculate the volume.

V = $\frac{m}{d}$ = 14 830 g × (1 cm³)/(19.32 g) = 767.6 cm³