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Chapter Overview
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Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
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Ratio
Proportion
Rates of change
Shapes
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Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Density is a measure of how heavy $1cm^3$ of a material is. Another way of saying this is that density is the mass per unit volume of a material. Every material has its own density.
The density of a material is given as:
$density=\frac{mass}{volume}$
Or, more simply:
$D=\frac{M}{V}$
Measurement | Units |
Density | kilograms per cubic metre ($kg/m^3$), grams per cubic centimetre ($g/cm^3$) |
Mass | kilograms ($kg$), grams ($g$) |
Volume | cubic metres ($m^3$), cubic centimetres ($cm^3$) |
To solve problems involving density, follow this procedure:
1. | Identify what values you have and what variable you want to find. |
2. | Rearrange the density formula for the desired variable. |
3. | Substitute in known values. |
4. | Give the answer with the correct units. |
The density of gold is $19{,}300kg/m^3$. A bar of gold weighs $4{,}000kg$. What is the volume of this bar to two decimal places?
From the given information, identify the density and the mass:
$D=19{,}300kg/m^3,\,M=4{,}000kg$
Write down the density formula:
$D=\frac{M}{V}$
Rearrange the density formula for volume:
$V=\frac{M}{D}$
Substitute in the known values:
$V=\frac{4000kg}{19300kg/m^3}$
Give the answer with the correct units:
$V=0.207253886...m^3$
Round to two decimal places, like the question asks:
$\underline{V=0.21m^3}$, to two decimal places.
Density is a measure of how heavy $1cm^3$ of a material is. Another way of saying this is that density is the mass per unit volume of a material. Every material has its own density.
The density of a material is given as:
$density=\frac{mass}{volume}$
Or, more simply:
$D=\frac{M}{V}$
Measurement | Units |
Density | kilograms per cubic metre ($kg/m^3$), grams per cubic centimetre ($g/cm^3$) |
Mass | kilograms ($kg$), grams ($g$) |
Volume | cubic metres ($m^3$), cubic centimetres ($cm^3$) |
To solve problems involving density, follow this procedure:
1. | Identify what values you have and what variable you want to find. |
2. | Rearrange the density formula for the desired variable. |
3. | Substitute in known values. |
4. | Give the answer with the correct units. |
The density of gold is $19{,}300kg/m^3$. A bar of gold weighs $4{,}000kg$. What is the volume of this bar to two decimal places?
From the given information, identify the density and the mass:
$D=19{,}300kg/m^3,\,M=4{,}000kg$
Write down the density formula:
$D=\frac{M}{V}$
Rearrange the density formula for volume:
$V=\frac{M}{D}$
Substitute in the known values:
$V=\frac{4000kg}{19300kg/m^3}$
Give the answer with the correct units:
$V=0.207253886...m^3$
Round to two decimal places, like the question asks:
$\underline{V=0.21m^3}$, to two decimal places.
FAQs
Question: What is the formula to calculate density?
Answer: The formula to calculate density is: Density = mass/volume.
Question: What is density?
Answer: Density is the mass of a material per unit volume.
Theory
Exercises
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