About This Chapter
Spherical Geometry - Chapter Summary
In this chapter, you can review details about calculating the arc length of a sector and the area and circumference of a circle. This material is presented in an easy and engaging way, using definitions, examples and illustrations to facilitate your learning experience. Lesson quizzes also provide you with the opportunity to practice the methods and formulas discussed to ensure that you fully understand the concepts being discussed. Once you have completed your review of this chapter, you should be able to do the following:
- Calculate the area and circumference of a circle
- Differentiate between major and minor arcs
- Understand how to measure an arc
- Describe how to measure the arc length of a sector
- Apply trigonometry and Pythagoras' theorem to solve right-angle triangles within a sphere
These video and text lessons offer a quick and effective way to reinforce what you might already know or to learn new facts about spherical geometry. Each lesson is accessible 24/7 from any device, so your studies will fit your busy schedule. Use the self-assessment quizzes to determine how much you have taken away from each lesson and whether you need further review in any of these topics.
1. Circles: Area and Circumference
Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.
2. Measure of an Arc: Process & Practice
What is the measure of an arc? And what is the difference between a minor arc and a major arc? Find out all that and practice finding the measure of an arc in this lesson.
3. Arc Length of a Sector: Definition and Area
In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.
4. Solving Right-Angled Triangles Within a Sphere
Triangles on the surface of a sphere need special considerations. In this lesson, we explore how great circles and distances are related when considering spherical right-angled triangles.
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Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
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- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
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- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Paths & Circuits
- Problem Solving With Networks
- Geometric Solids
- Measurement & Trigonometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
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