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Which three go together? Why do they go together?
Your teacher will give your group two circles of different sizes.
For each circle,
| diameter (cm) | estimated area (cm2) |
|---|---|
Plot your diameter and area values on the coordinate plane. What do you notice?
Earlier, you graphed the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?
Your teacher will give you a page with two circles on it and a piece of paper that is a different color.
Follow these instructions to create a visual display:
Cut out both circles, cutting around the thick outline.
Fold and cut one of the circles into fourths.
Arrange the fourths so that straight sides are next to each other, but the curved edges are alternately on top and on bottom.
Pause here so your teacher can review your work.
Fold and cut the fourths in half to make eighths. Arrange the eighths next to each other, like you did with the fourths.
Pause here so your teacher can review your work.
After you finish gluing your shapes, answer the following questions.
How do the areas of the two shapes compare?
What polygon does the shape made of the circle pieces most resemble?
How could you find the area of this polygon?
Imagine a circle made of rings that can bend, but not stretch.
The circumference
The area of a circle can be found by taking the product of half the circumference and the radius.
If
This equation can be rewritten as:
Remember that when we have
This means that if we know the radius, we can find the area. For example, if a circle has a radius of 10 cm, then its area is about
If we know the diameter, we can figure out the radius, and then we can find the area. For example, if a circle has a diameter of 30 ft, then the radius is 15 ft, and the area is about
The area of a circle is the number of square units it covers. If a circle has radius
For example, a circle has radius of 3 inches. Its area is
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