# ﻿Circumference and Wheels

Warmup

Activity #1

Investigate the Relation Between the Diameter and Circumference of a Circle. • Roll the circle on a line by dragging the Roll slider. What does does the red line represent?
• Check the circle diameters to display them on the circles.
• Now, check the diameter lengths to locate them on the line.
• Compare the diameter lengths to the entire length of the red line.

What do you notice about their lengths?

• Use your ruler to measure each distance.
• Record these values in the first row of the table below.

If you wanted to trace two complete rotations of your object, how long of a line would you need?

Activity #2

Investigate the Relation Between the Diameter and Circumference of a Circle. • Drag the blue point in the center of the wheel to move it. You can click and drag the background to shift your view.
• Use the mouse wheel to zoom in and out if necessary.
• Choose a measurement for the radius of the wheel(not more than 40 recommended), and roll the wheel out.

(3.) How far did the wheel roll out?

• Repeat the process with three more measurements .

(6.) Find the circumference of a wheel with radius 25cm.

Activity #3

More about the Relation Between Circumference and Diameter.

In this activity, you are going to measure the circumference of a circle by unrolling it into a straight line. Then you’ll explore the relationship between its circumference and diameter. • Use the line tool and the distance tool to verify that the diameter of the circle is 3.1 units.
• Now, drag the center of the circle to unroll it. When it is completely unrolled, the circumference is automatically displayed.
• Drag the slider all the way to the right to find out how many times the diameter fits in the circumference.
• Use the line tool and distance tool again to verify that the circumference is approximately 9.7 units.
• Now, divide the circumference by the diameter and record your value.
• Reset and change the diameter using the point on the circle. ​
• Repeat the steps above for six different values of the diameter.

(1.) Are the values you obtain after division fairly constant?

(2.) What might be a source of any differences in value?

Challenge #1

Use the tire radius slider to choose the size of the circle. Use the tire spin slider to unroll the circle. Answer the question.

Challenge #2

The length of segment AE is 5 centimeters.

(1.) What is the length of segment  C D ?

(2.) What is the length of segment A B ?

(3.) Name a segment that has the same length as segment A B.

Challenge #3

A bike wheel has a radius of 13 inches.

(1.) About how far does the bike wheel travel in 1 rotation? 5 rotations? 30 rotations?

(2.) Using the same bike wheel as above, write an equation relating the distance the bike travels in inches, , to the number of wheel rotations, (3.) About how many rotations does the bike wheel make when the bike travels 1 mile? Explain or show your reasoning.

Quiz Time