Meaning of π & its connection to the circumference

Note: LARGE WHITE POINT is MOVEABLE.

1.

How many diameters were we able to wrap perfectly around this circle? [br](Round your answer to the nearest 0.01.)

2.

Move the LARGE WHITE POINT a bit (to change the size of the circle). Does your answer to question (1) change at all?

3.

Does your response for (1) look familiar? Where you have you seen this number before?

Quick (Silent) Demo

4. Making connections - Diameter and circumference

Based on what we have explored, if the diameter of a circle = 5 cm, what is the calculation required to determine the circumference [math]C[/math] of this circle (measurement around the circle)?

[math]C=10\pi[/math] [math]C=\pi[/math] [math]C=5\pi[/math] [math]C=\pi+5[/math]

5 Diameter and Circumference in your own words

[b]In your own words[/b], explain how to find the circumference [math]C[/math] of ANY circle if we know the diameter [math]d[/math]

6. Making connections - radius and circumference

We know that the radius is half of the diameter, or equivalently that the diameter is double the radius.[br]This can be expressed as:[br] [math]r=\frac{d}{2}[/math] or [math]d=2r[/math][br][br]What is the calculation required to determine the circumference [math]C[/math] of a circle with a radius = 3.5m?

[math]C=\frac{3.5}{2\pi}[/math] [math]C=3.5\cdot\pi[/math] [math]C=2\cdot3.5\cdot\pi[/math] [math]C=\frac{3.5}{\pi}[/math]

7. Radius and Circumference in your own words

[b]In your own words[/b], explain how to find the circumference [math]C[/math] of ANY circle if we know the radius [math]r[/math]