Unit 10: Circles Homework 3: Arc Lengths Solutions
This page presents solutions to various problems related to finding arc lengths in circles. The worksheet covers a range of scenarios, from basic arc length calculations to more complex applications.
Definition: Arc length is the distance along a curved line segment of a circle.
The problems on this page demonstrate the application of the arc length formula:
Formula: Arc Length (l) = (central angle / 360°) × (2πr)
Where r is the radius of the circle and the central angle is measured in degrees.
Notable problem types include:
- Calculating arc lengths given radius and central angle
- Finding missing arc lengths when other circle measurements are provided
- Applying arc length concepts to real-world situations
Example: Problem 8 involves calculating the distance traveled by a clock's minute hand, combining time and angular measurements.
Highlight: Problem 9 presents a reverse calculation, determining the angle of rotation for a Ferris wheel given the arc length traveled.
The solutions demonstrate step-by-step calculations, often requiring rounding to specified decimal places. This worksheet serves as an excellent practice tool for students learning about arc lengths solutions in unit 10 lesson 3.
Vocabulary:
- Central angle: The angle formed at the center of a circle by two radii
- Diameter: A straight line passing through the center of a circle, with its endpoints on the circle's circumference
This comprehensive set of problems provides a thorough review of arc length calculations, preparing students for more advanced geometry concepts related to circles.