Lesson 7Exploring the Area of a Circle
Learning Goal
Let’s investigate the areas of circles.
Learning Targets
I know whether or not the relationship between the diameter and area of a circle is proportional and can explain how I know.
If I know a circle’s radius or diameter, I can find an approximation for its area.
Lesson Terms
- area of a circle
Warm Up: Estimating Areas
Problem 1
Your teacher will show you some figures. Decide which figure has the largest area. Be prepared to explain your reasoning.
Activity 1: Estimating Areas of Circles
Problem 1
Your teacher will assign your group two circles of different sizes.
Set the diameter of your assigned circle and use the applet to help estimate the area of the circle.
Note: to create a polygon, select the Polygon tool, and click on each vertex. End by clicking the first vertex again. For example, to draw triangle
, click on - - - . Record the diameter in column
and the corresponding area in column for your circles and others from your classmates. In a previous lesson, you graphed the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?
Print Version
Your teacher will give your group two circles of different sizes.
For each circle, use the squares on the graph paper to measure the diameter and estimate the area of the circle. Record your measurements in the table.
diameter (cm)
estimated area (cm
) Plot the values from the table on the class coordinate plane. Then plot the class’s data points on your coordinate plane.
In a previous lesson, you graphed the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?
Are you ready for more?
Problem 1
If you get stuck, consider using coins or other circular objects.
How many circles of radius 1 unit can you fit inside a circle of radius 2 units so that they do not overlap?
How many circles of radius 1 unit can you fit inside a circle of radius 3 units so that they do not overlap?
How many circles of radius 1 unit can you fit inside a circle of radius 4 units so that they do not overlap?
Activity 2: Covering a Circle
Problem 1
Here is a square whose side length is the same as the radius of the circle.
How many of the squares do you think it would take to cover the circle exactly?
Lesson Summary
The circumference
The area of a circle with radius
The area