🎓 Deeper Dive — Adults

3D solids extend 2D shapes with depth. Key formulas:

Cube V = s³, SA = 6s². Cuboid V = lwh. Sphere V = (4/3)πr³, SA = 4πr². Cylinder V = πr²h. Cone V = (1/3)πr²h.

Euler's formula for convex polyhedra: F + V = E + 2 (faces + vertices = edges + 2).

Volume of any solid = ∫ A(x) dx where A(x) is the cross-section area — the basis of integration.