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Session 7, Part B:
Area of a Circle
In This Part: Transforming a Circle | Examining the Formula
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Let's further examine the formula for area of a circle, A =  • r2. How do we interpret the symbols r2? If r is the radius of a circle, then r2 is a square with sides of length r. Examine the circles below. A portion of each circle is covered by a shaded square. We can call each of these squares a radius square.
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Problem B5 | |
Use the circles (PDF document) to work on this problem. For each circle, cut out several copies of the radius square from a separate sheet of centimeter grid paper. Determine the number of radius squares it takes to cover each circle. You may cut the radius squares into parts if you need to. Record your data in the table below.
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Circle |
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Radius of Circle |
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Area of Radius Square |
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Area of Circle |
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Number of Radius Squares Needed |
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1 |
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6 |
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36 |
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36 • |
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A little more than 3. |
2 |
4 |
16 |
16 • |
A little more than 3. |
3 |
3 |
9 |
9 • |
A little more than 3. |
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Problem B6 |  |
a. | What patterns do you observe in your data? |
b. | If you were to estimate the area of any circle in radius squares, what would you report as the best estimate? |
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Problem B7 |  |
Does the activity of determining the number of radius squares it takes to cover a circle provide any insights into the formula for the area of a circle? |
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Problem B8 | |
When you enlarge a circle so that the radius is twice as long (a scale factor of 2), what do you think happens to the circumference and the area? Do they double? Experiment by enlarging circles with different radii and analyzing the data. |
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