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

m = d×V

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

DENSITY

Density is defined as mass per unit volume.

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

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