# Exploring Circumference

Warmup

Clare wonders if the height of the toilet paper tube or the distance around the tube is greater.

What information would she need in order to solve the problem? How could she find this out?

Activity #1

Measure the Circumference of a Circle.

When the tire of a bike turns one complete revolution, the bike travels a distance equal to the circumference of the tire. Here below is a visualization to help you understand how that happens. • Just “unroll” using the slider in the applet below until the red spot on the circle touches the ruler again. Just exactly when the red spot hits the ruler again, you see the diameter appear.
• Explore the applet using 6 different values of the diameter and enter your values in the table below. In other to stay within screen view, choose values for the diameter that are not more than 8 units.

• Use the line tool , and the measurement tool in the applet below to find diameter and circumference of the three circles.
• Record the diameter and circumference of the circles to the nearest tenth of a unit.

• Plot the diameter and circumference values from the table in the last activity above, on the following coordinate plane.

What do you notice?

Activity #2

Find the Missing Distance.

Here below are five circles. One measurement for each circle is given in the table. • Use the constant of proportionality estimated in the previous activity to complete the table below. Activity #3

Explore a Circle to Find the Value of Pie. • Drag the green sign on the circle to appropriate position to measure the diameter of the circle.

What is its diameter?

• Drag the red sign, P to straighten the circumference. You may divide the scale of the ruler to measure its length to two decimal places.
• Now, using the slider, change the diameter of the circle to 2 cm, 3 cm, or any other diameters.

(1.) Calculate the value of: circumference ÷ diameter.

(2.) What do you notice?

Challenge #1

Diego measured the diameter and circumference of several circular objects and recorded his measurements in the table.

One of his measurements is inaccurate. Which measurement is it? Explain how you know.

Challenge #2

The circumference of Earth is approximately 40,000 km. If you made a circle of wire around the globe, that is only 10 meters (0.01 km) longer than the circumference of the globe, could a flea, a mouse, or even a person creep under it?

Challenge #3

Complete the table. Use one of the approximate values for pi discussed in class (for example 3.14, 22/7, 3.1416).

Explain or show your reasoning for how you determined the missing values in the table.

Quiz Time 