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# 8.9: Composite Area and Change of Dimensions

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## Learning Objectives

• Use similarity to generalize the results.

## Similarity

We know that all circles are similar to each other.

Suppose a circle has a radius of $r$ units.

• The scale factor of this circle (with radius $r$ ) and the circle with radius 1 is:

$r : 1, \quad \frac{r}{1}, \quad \text{or just} \quad r$.

• You know how a scale factor affects area measures:

If the scale factor is $r$, then the area is $r^2$ times as much.

1. Explain how we know that all circles are similar to each other.

(Hint: Think about similar measurements that circles may have.)

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2. If the scale factor of a circle is $r$, how does this relate to a circle’s area?

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## Date Created:

Feb 23, 2012

May 12, 2014
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