Unit 7
Three-dimensional measurement and a look at how geometry itself is built from axioms. Composite solids are decomposed into parts whose measures add.
Lesson 7.1
Volume measures enclosed space in cubic units; surface area measures exposed faces in square units. For a prism use the area of its base times its perpendicular height. For a cone or pyramid include the factor one-third.
Lesson 7.2
A cross section is the intersection of a solid with a plane. Its shape depends on the direction of the cut. For similar solids, lengths, surface areas, and volumes scale by the first, second, and third powers of the same factor.
Lesson 7.3
An axiomatic system begins with undefined terms, definitions, and accepted postulates. Theorems follow by deduction. A proof must use the chosen system: Euclidean parallel-line results need not hold on a sphere.
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