Solid geometry (other)

Solid geometry (other) covers three-dimensional shapes beyond the standard polyhedra and solids of revolution. This includes composite solids (formed by combining or subtracting basic solids), solids with holes or cutouts, and solids with unusual bases or cross-sections. Problems often require decomposing a complex solid into simpler parts, or using symmetry and spatial reasoning.

Important properties

• Volumes and surface areas of composite solids can be found by adding or subtracting the volumes/surface areas of simpler solids.

• Cavalieri's Principle: If two solids have equal heights and equal cross-sectional areas at every level, they have equal volumes.

• Symmetry and congruence can simplify calculations for irregular or composite solids.