Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Why the circle and solid formulas hold
Justify circle cylinder cone and pyramid formulas using dissection and comparison
Problem types
- Justify circle and solid measurement formulas
- Cone and pyramid cross-section and volume
- Volume of a slanted stack of coins
Builds on
Leads to
- Cavalieri's principle
- Modeling with geometry · See it applied
Justified area and volume formulas are used to model objects, such as a regular polygon whose area splits into triangles.
- Area from two sides and the included angle · Extend the idea
The area formula one half base times height becomes one half ab sin C when the height is written with a sine.
Related skills
- Volume of cylinders, cones, and spheres · Shared foundations
- Arc length and sector area · Shared foundations
- Theorems about circles · Shared foundations
- Congruence criteria for triangles · Shared foundations
- Proofs that use coordinates · Shared foundations
Open the interactive map to explore lessons and skill connections.