Illuminations: Circle Tool

# Circle Tool

How do the area and circumference of a circle compare to its radius and diameter? This activity allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section.

### Instructions

 In the Intro section, explore the relationship of the circumference to the radius and diameter. Play the movie clip to visually see how they are related. In the Investigation section, collect data points by dragging the radius to various lengths, and the click the "Add to Table" button to record the data in the table. By default, the radius, diameter, circumference and area are shown in a table. Clicking on the x/y button allows you to examine the relationship between any two measures. Clicking on the graph button will take you to a graph of the data. You can plot any of the four measures on the x-axis against any of the four measures on the y-axis. In the Problems section, determine the answer to each question using the applet, a calculator, or paper and pencil. And don't forget to indicate the proper units!

### Exploration

 Can you determine the relationship between… …radius and diameter? …radius and circumference? …diameter and circumference? …radius and area? Some relationships can be discovered using the x/y button. Others will require more investigation, but the graph should give you some insight.

### NCTM Resources

 Principles and Standards for School Mathematics (Book and E-Standards CD)

### Lessons

 More and Better Mathematics for All Students
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