Unit 3, Lesson 7
Exploring the Area of a Circle
Grade 7
7.1
Warm-up
Which Three Go Together: Figures on a Grid
Which three go together? Why do they go together?
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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?
A coordinate plane with the origin labeled O. The horizontal axis is labeled "diameter, in centimeters," and the numbers 5 through 25, in increments of 5, are indicated. The vertical axis is labeled "area, in square centimeters, and the numbers 50 through 300, in increments of 50, are indicated.
Earlier, you graphed the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?
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?
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