Exploring the Area of a Circle

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Estimate the Area of a Circle.

Set the diameter of each circle 5, 7, 8, 10 using the slider, and use the applet to help estimate the area of the circle.

Record the diameter in column D and the corresponding area in column A for your circles.

In a previous lesson, you established the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?

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Explore the Area of a Circle.

  • Drag the slider to the end to straighten the circumference of the circle.
  • Check the circumference box.
  • Click the dissect checkbox to dissect the circle.
  • Rearrange the dissected parts using the green slider. What shape does the figure look like when you rearrange it?
  • You can increase number of parts using the red slider. As you increase the number of parts, what does the figure begin to look like? What are the dimensions of that shape? What is the formula for the area of that shape?

(1). Find the area of a circle whose radius is 7 cm.

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Explore the Area of a Circle in Relation to the Diameter.

Here is a picture of two squares and a circle.

Here is another picture of two squares and a circle.

Use the picture above to explain why the area of the circle is more than 2 square units but less than 4 square units.

Use the picture above to explain why the area of this circle is more than 18 square units and less than 36 square units.

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Here is a square whose side length is the same as the radius of the circle.

How many of these squares do you think it would take to cover the circle exactly?

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Point A  is the center of the circle, and the length of  C D is 15 centimeters. Find the circumference of this circle.

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The x-axis of each graph has the diameter of a circle in meters. Label the y-axis on each graph with the appropriate measurement of a circle by dragging the labels.