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Math · Intermediate

3D Shapes

Step into three dimensions. Meet the five perfect Platonic solids, discover Euler's surprising formula linking vertices, edges and faces, learn why a cone holds exactly a third of a cylinder and a sphere two-thirds, slice a cube into hexagons, unfold solids to find shortest paths, stack spheres as tightly as possible, and step into the fourth dimension.

7 lessons~40 min0/7 complete
1

Polyhedra

Flat-faced solids.

  1. Platonic SolidsThe five perfect shapes
  2. Euler’s FormulaV − E + F = 2
2

Volume

Cones, cylinders and spheres.

  1. Cones, Cylinders, SpheresArchimedes’ favourite result
3

Slicing and Unfolding

Cross-sections, nets and shortest paths.

  1. Cross-SectionsWhat’s inside a cube?
  2. Nets & Shortest PathsUnfold a solid to understand it
4

Packing and Higher Dimensions

Stacking spheres, and cubes beyond three dimensions.

  1. Packing SpheresThe greengrocer’s problem
  2. The Fourth DimensionHypercubes by analogy