How are density mass and volume related?

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Answer 1 · 2014-01-11T01:42:56

They are related by the the density triangle.

They are related by the the density triangle.

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d = #m/V#

m = d×V

V = #m/d#

DENSITY

Density is defined as mass per unit volume.

d = #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 = #m/V# = #(433 g)/(200 cm³)# = 2.16 g/cm³

MASS

d = #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 × #(1.11 g)/(1 mL)# = 555 g

VOLUME

d = #m/V#

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

V = #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 × #(1000 g)/(1 kg)# = 14 830 g

Step 2: Calculate the volume.

V = #m/d# = 14 830 g × #(1 cm³)/(19.32 g)# = 767.6 cm³