Converting a radius into a length depends on the specific context and what kind of length you're trying to find. Here are the most common scenarios:
1. Finding the Circumference of a Circle
The most straightforward conversion is finding the circumference of a circle.
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Formula: Circumference (C) = 2 π radius (r)
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Where:
- π (pi) is approximately 3.14159
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Example: If the radius of a circle is 5 units, the circumference is 2 π 5 ≈ 31.4159 units.
2. Finding the Diameter of a Circle
The diameter is simply twice the radius.
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Formula: Diameter (D) = 2 * radius (r)
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Example: If the radius is 7 units, the diameter is 2 * 7 = 14 units.
3. Finding the Arc Length
If you have a central angle (θ) and a radius (r), you can find the arc length. The angle must be in radians for this to work directly.
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Formula (Angle in Radians): Arc Length (s) = θ * r
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Formula (Angle in Degrees): Arc Length (s) = (θ π / 180) r
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Example (Radians): If the radius is 10 units and the central angle is 0.5 radians, the arc length is 0.5 * 10 = 5 units.
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Example (Degrees): If the radius is 10 units and the central angle is 30 degrees, the arc length is (30 π / 180) 10 ≈ 5.236 units.
4. Other Contexts
If you're thinking about something other than circles or arcs, please specify the context. For example, you might be referring to:
- The radius of a sphere: In this case, you might want to calculate the surface area or volume.
- A radius within a geometric shape: The "length" you are trying to derive will depend on the properties of the shape.
In summary, the conversion depends on what "length" you are trying to calculate from the radius. Circumference, diameter, and arc length are the most common interpretations.
