Surface area

Volume

Geometric transformations

MYP Standard Mathematics Volume Notes

Volume Units Work Differently From Length Units

For length, each step (for example from m to cm) is a factor of 100.

For area, each step is squared.

For volume, each step is cubed.

That single idea explains most volume conversions.

Why Squared And Cubed Units Grow So Fast

If you scale a shape by a factor of $k$:

Lengths scale by $k$
Areas scale by $k^2$
Volumes scale by $k^3$

So changing from meters to centimeters multiplies lengths by $100$, but multiplies volumes by $100^3=1{,}000{,}000$.

Common Mistake

A very common mistake is to convert m$^3$ to cm$^3$ by multiplying by 100 or 10,000.
For volume you must cube the linear conversion factor.

Cubes Make Unit Conversion Visual

A cube is the easiest solid for understanding volume because its volume is side$^3$.

Converting m$^3$ And cm$^3$

Since $1\text{ m}=100\text{ cm}$,

a cube of side $1\text{ m}$ has volume $1\text{ m}^3$
a cube of side $100\text{ cm}$ has volume $(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3$

So, $$1\text{ m}^3=1{,}000{,}000\text{ cm}^3$$

Converting cm$^3$ And mm$^3$

Since $1\text{ cm}=10\text{ mm}$, $$1\text{ cm}^3=(10\text{ mm})^3=1000\text{ mm}^3.$$

So:

cm$^3$ to mm$^3$: multiply by $1000$

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MYP Standard Mathematics Volume Notes

Volume Units Work Differently From Length Units

Why Squared And Cubed Units Grow So Fast

Cubes Make Unit Conversion Visual

Converting m$^3$ And cm$^3$

Converting cm$^3$ And mm$^3$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Volume Units Work Differently From Length Units

Why Squared And Cubed Units Grow So Fast

Cubes Make Unit Conversion Visual

Converting m$^3$ And cm$^3$

Converting cm$^3$ And mm$^3$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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Number and Algebra Foundations7 subtopics

Coordinate Geometry and Linear Modelling5 subtopics

Functions and Quadratic Relationships4 subtopics

Sets, Logic and Probability4 subtopics

Geometry of Shapes, Surface Area and Volume3 subtopics

Statistical Measures and Data Representation3 subtopics

Right Triangles and Circle Geometry3 subtopics

Sequences, Formulae and Proportional Reasoning3 subtopics

Sampling Methods and Bivariate Data2 subtopics

MYP Standard Mathematics Volume Notes

Number and Algebra Foundations7 subtopics

Coordinate Geometry and Linear Modelling5 subtopics

Functions and Quadratic Relationships4 subtopics

Sets, Logic and Probability4 subtopics

Geometry of Shapes, Surface Area and Volume3 subtopics

Statistical Measures and Data Representation3 subtopics

Right Triangles and Circle Geometry3 subtopics

Sequences, Formulae and Proportional Reasoning3 subtopics

Sampling Methods and Bivariate Data2 subtopics

Volume Units Work Differently From Length Units

Why Squared And Cubed Units Grow So Fast

Cubes Make Unit Conversion Visual

Converting m$^3$ And cm$^3$

Converting cm$^3$ And mm$^3$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Volume Units Work Differently From Length Units

Why Squared And Cubed Units Grow So Fast

Cubes Make Unit Conversion Visual

Converting m$^3$ And cm$^3$

Converting cm$^3$ And mm$^3$

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account