§7 Introduction to Solid Geometry
Solid geometry — also called stereometry — is the study of three-dimensional figures: their structure, properties, surface areas, and volumes. Moving from the plane into space requires new axioms, new ways of thinking about parallelism and perpendicularity, and a richer vocabulary of shapes.
Learning Objectives
By the end of this chapter you will be able to:
- State and apply the fundamental axioms of solid geometry
- Classify the relative positions of two lines, a line and a plane, and two planes in space
- Define and identify skew lines, and find the angle between them
- Define perpendicularity of a line to a plane and apply the perpendicularity criterion
- Understand dihedral angles and how to measure them
- Calculate the lateral surface area, total surface area, and volume of a right prism and a regular pyramid
- Calculate the lateral surface area, total surface area, and volume of a cylinder, cone, and sphere
- Apply Cavalieri’s principle to justify volume formulas