Public learning track
Cavalieri's Principle and Spatial Measurement of 3D Solids
9th Grade · Math · Open Global Math
10 lessons
Goal
Use Cavalieri's principle and solid decomposition methods to derive and calculate surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids.
Featured Diagrams
Understanding Cavalieri's Principle for 2D and 3D Figures
10 lessons
0 of 10 done
- 1Understanding Cavalieri's Principle for 2D and 3D FiguresUp nextStart
- 2Volume and Surface Area of Right and Oblique PrismsPremiumNot started yet
- 3Volume and Surface Area of Right and Oblique CylindersNot started yet
- 4Deriving Pyramid Volume Through Cube DecompositionNot started yet
- 5Deriving the Curved Surface Area of a Cone Using a SectorNot started yet
- 6Surface Area of Pyramids and ConesNot started yet
- 7Deriving the Volume and Surface Area of a Sphere Using Cavalieri's PrincipleNot started yet
- 8Comparing Volumes of Cylinders, Cones, and SpheresNot started yet
- 9Volume and Surface Area of FrustumsNot started yet
- 10Word Problems: Surface Areas and Volumes of Combined SolidsNot started yet
Curriculum Framework
9th Grade · Math · Open Global Math
1
7 lessons
The Pythagorean Theorem: Geometric Proofs, Converse, and Applications
Master geometric and similarity-based proofs of the Pythagorean theorem, use its converse to classify triangles, and solve complex multi-step geometric problems.
2
9 lessons
Foundations of Right Triangle Trigonometry
Establish sine, cosine, and tangent ratios through triangle similarity, derive exact trigonometric values for special angles, and utilize fundamental trigonometric identities.
3
7 lessons
Right Triangle Trigonometry: Solving Triangles and Real-World Applications
Solve unknown sides and angles in right triangles and apply trigonometric techniques to solve complex multi-step real-world problems.
4
5 lessons
Circle Metrics: Arc Length, Sectors, and Circular Segments
Derive and calculate arc length, sector area, and circular segment area in degrees and radians, and solve composite geometric problems.
5
10 lessons
Cavalieri's Principle and Spatial Measurement of 3D Solids
Use Cavalieri's principle and solid decomposition methods to derive and calculate surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids.
6
7 lessons
Cartographic Map Projections and Metric Distortions
Analyze how mapping a 3D spherical surface onto 2D planes induces metric distortions in angles, scale, and surface area across cylindrical, conic, and azimuthal projections.