6 Questions
What is the primary factor that determines the length of an arc?
The central angle of the arc
What is the formula to calculate the arc length?
L = (θ/360) × 2 × π × r
What unit is typically used to measure arc length?
Meters
In which field is arc length used to measure distances along curved boundaries?
Geography
What happens to the arc length if the radius of the circle is halved?
The arc length is halved
What is an arc in the context of a circle?
A part of a circle bounded by two distinct points
Study Notes
Arc Length
Definition
- An arc is a part of a circle bounded by two distinct points on the circle, called the endpoints of the arc.
- Arc length is the distance along the circle between the endpoints of the arc.
Formula
- The arc length (L) can be calculated using the central angle (θ) and the radius (r) of the circle:
- L = (θ/360) × 2 × π × r
- θ is measured in degrees
- r is the radius of the circle
Units
- Arc length is typically measured in units of length, such as meters (m), centimeters (cm), or inches (in).
Real-World Applications
- Arc length is used in various fields, including:
- Architecture: designing circular structures, such as columns or arches
- Engineering: calculating stresses and loads on curved surfaces
- Geography: measuring distances along curved boundaries, such as coastlines or rivers
Key Concepts
- The longer the arc, the larger the central angle.
- The shorter the radius, the shorter the arc length for a given central angle.
Test your understanding of arc length, including its definition, formula, units, and real-world applications in architecture, engineering, and geography.
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