Learn to compute volumes and surface areas for complex solids, analyze relations between lines and planes in 3D, and apply dot/cross products to solve real engineering problems.
Compute volumes and surface areas for composite solids with shared faces.
Model capacity and material usage in engineering design tasks.
Analyze line-plane relations: intersection, parallelism, and angles.
Use dot and cross products for angles, areas, and physical interpretations.
Lesson 3-1
Composite solids, volume/surface computations, shared-face adjustments, and engineering design contexts.
Lesson 3-2
3D coordinate geometry, distances, line/plane equations, and intersection/parallelism analysis.
Lesson 3-3
Vector arithmetic, dot and cross products, angles, areas, and real-world applications.
Volume and surface computations inform capacity, materials, and cost in product design.
Spatial relations (line-plane) underpin CAD modeling and physics problem solving.
Dot and cross products connect geometry, mechanics, and electromagnetism.