# Exploring the Area of a Circle

Warmup

Activity #1

Estimate the Area of a Circle. • Set the diameter of each circle to be 4, 6, 8, 10, and 12 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.

(1.) How is this graph the same?

(2.) How is it different?

Activity #2

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.
• Separate the dissected parts by moving the green slider half way through.

(1.) What shape does the figure look like when you rearrange the bisected parts?

• Move the red slider back and forth to see how possible number of sectors.
• Now, move the slider all the way to the end.

(2.) What does the figure begin to look like?

• Move the red slider all the way to the right.

(3.) What are the dimensions of the new shape?

(4.) What is the formula for the area of that shape?

Activity #3

Explore the Area of a Circle in Relation to the Diameter. • Study the following two pictures and answer the questions that follow.

Here is a picture of two squares and a circle.

(1.) Use any tools in the applet above that can help you to explain why the area of the circle is more than 2 square units but less than 4 square units.

Here is another picture of two squares and a circle.

(2.) Use any tools in the applet above that can help you to explain why the area of this circle is more than 18 square units and less than 36 square units. Challenge #1

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?

Challenge #2

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

Challenge #3

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.

Quiz Time 