8.5 A volumes of enlargements

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• Middelbare school
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• Leerjaar 2

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Today

You understand what happens to the volume of a figure when it's enlarged and are able to perform calculations accordingly.

Consider these two cubes.

What is the scale factor?

1. 6
2. 36
3. 2
4. 3

Consider these two cubes.

The volumes of the cubes are:

2⋅2⋅2=8

12⋅12⋅12=1728

The volumes of the cubes are:

Now,

So the volume has 
increased 216 fold
with k = 6.

2⋅2⋅2=8

12⋅12⋅12=1728

​8​​1728​​=216

With a scale factor of 6,

the volume is multiplied by 216.

These numbers are related:

6​3​​=216

With a scale factor of 6,

the volume is multiplied by 216.

When a 3D figure is enlarged by a factor k,

its volume is increased by a factor k³.

6​3​​=216

When a 3D figure is enlarged by a factor k,

its volume is increased by a factor k³.

This statement can be reversed. If the volume of the enlargement is p times as big, the scale factor is the cube root of p:

This statement can be reversed. If the volume of the enlargement is p times as big, the scale factor is the cube root of p:

So when we know a drum holds a 1000 times as much water compared to a smaller drum, the scale factor is 

Practice!

31, 33, 35, 37

40, 42, 46, 50

53, 56, 61, 63

64, 67, 69, 70