Circumference and Wheels


Investigate the Relation Between the Diameter and Circumference of a Circle.

  • Roll the circle on a line by dragging the Roll slider. The 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.

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


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.

(2). Choose a measurement for the radius of the wheel and roll the wheel out(not more than 40 recommended). How far did the wheel roll out?
(3). Repeat the process with three more measurements .

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


More about the Relation Between Circumference and Diameter.

Measure the circumference of the circle by unrolling it into a straight line. Explore the relationship between the circumference and the diameter of the circle.

  • Drag the center of the circle to unroll it.
  • Change the diameter using the point on the circle. ​
  • Drag the slider to find out how many times the diameter fits in the circumference.


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


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.


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.