📚 Practice With Worksheets
Practice finding circumference, using diameter and radius, and applying circle formulas with these related worksheets.
▶️ Learn With Videos
Review circumference formulas, connect radius and diameter, and solve circle problems when different measurements are provided.
🛠️ How to Use This Tool
Drag the diameter slider to make the circle expand or contract and observe how its measurements change.
Watch how the radius changes automatically because the radius is always one-half of the diameter.
Compare the displayed diameter, radius, circumference, and circumference-to-diameter ratio to investigate how these quantities are related.
🧠 Things to Notice
When the diameter doubles, the circumference also doubles because circumference and diameter have a proportional relationship.
The ratio of circumference to diameter remains approximately 3.14 for every circle. This constant ratio is called pi.
Circumference is measured in linear units because it represents the distance around the outside of a circle.
📘 Vocabulary
Circle: The set of all points in a plane that are the same distance from a center point.
Center: The point inside a circle that is the same distance from every point on the circle.
Radius: The distance from the center of a circle to any point on the circle.
Diameter: The distance across a circle through its center.
Circumference: The distance around the outside of a circle.
Perimeter: The distance around a two-dimensional figure.
Pi: The constant ratio of a circle’s circumference to its diameter.
Linear Unit: A unit used to measure length or distance, such as inches, feet, centimeters, or meters.
Ratio: A comparison of two quantities using division.
Formula: A mathematical rule written with numbers, symbols, or variables.
📐 Circumference Rules
Circumference measures the distance around a circle. Before selecting a formula, identify whether the problem gives the diameter, radius, circumference, or another circle measurement.
Using the diameter: Multiply the diameter by pi when the distance across the center of the circle is known.
\(C=\pi d\)
Using the radius: Since the diameter is twice the radius, multiply \(2\), pi, and the radius.
\(C=2\pi r\)
Radius and diameter: The diameter is twice the radius, while the radius is one-half of the diameter.
\(d=2r\)
\(r=\frac{d}{2}\)
The meaning of pi: Dividing the circumference of any circle by its diameter produces the constant ratio pi.
\(\frac{C}{d}=\pi\)
Finding a missing diameter: Divide the circumference by pi when the circumference is known.
\(d=\frac{C}{\pi}\)
Finding a missing radius: Divide the circumference by \(2\pi\), or first find the diameter and then divide it by two.
\(r=\frac{C}{2\pi}\)
A circumference answer should be written in linear units, such as centimeters or inches. Use the pi button for an exact calculator value, or use \(3.14\) when the problem specifically asks for that approximation.
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