The way that scale factor affects volume is different from the way that it affects area or perimeter.

Let's look at how scale factor affects volume.

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How does the scale factor affect volume?
Volume is the product of length width and height (on a rectangular prism to get volume multiply the length width and height), so let's look at some examples of how scale factor affects the product of three numbers:

For example:

$\[ 7 \times 5 \times 3 = 105 \]$

The volume is 105

Suppose the scale factor is 2

$\[ 14 \times 10 \times 6 = 840 \]$

The volume is 840

When we used a scale factor of two did that double the volume or did it cause the volume to be multiplied by 8?

Since
$\[ 105 \times 8 = 840 \]$

We can see that the volume was multipled by 8


Another example:

$\[ 12 \times 8 \times 6= 576 \]$

The volume is 576

Suppose the scale factor is one half

$\[ 6 \times 4 \times 3 = 72 \]$

The volume is 72

When we used a scale factor of one half did that half the volume or did it cause the volume to be multiplied by one eighth?

Since
$\[ 576 \times \frac{1}{8} = 72 \]$

We can see that the volume was multipled by one eighth.

Volume units do change( if the sides are in feet then the volume is measured in cubed feet; cubed feet is the same as feet times feet times feet)




Student exlanation:


Remember


Volume is changed by (scale factor times scale factor times scale factor)



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