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3D Geometry: Volume & Surface Area

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Volume and surface area formulas for 3D solids.

geometry3dvolumesurface-area

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Solid geometry

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  1. 1Solid geometry
    The geometry of three-dimensional Euclidean space (3D space)
  2. 2Another name for solid geometry
    Stereometry
  3. 3Solid figure
    The region of 3D space bounded by a two-dimensional closed surface
  4. 4Polyhedron
    A solid whose boundary consists of flat polygonal faces, sharp vertices, and straight edges
  5. 5Prism
    A polyhedron with two parallel congruent polygonal bases connected by parallelogram faces
  6. 6Pyramid
    A polyhedron with a polygonal base and triangular faces meeting at an apex
  7. 7Cube
    A regular polyhedron with six square faces
  8. 8Cuboid
    A box-shaped polyhedron with six rectangular faces (also called rectangular prism)
  9. 9Parallelepiped
    A prism whose base is a parallelogram; all six faces are parallelograms
  10. 10Tetrahedron
    A pyramid with a triangular base, having four triangular faces
  11. 11Regular tetrahedron
    A tetrahedron with four equilateral triangular faces
  12. 12Octahedron
    A polyhedron with eight faces
  13. 13Regular octahedron
    A polyhedron with eight equilateral triangular faces
  14. 14Dodecahedron
    A polyhedron with twelve faces
  15. 15Regular dodecahedron
    A polyhedron with twelve regular pentagonal faces
  16. 16Icosahedron
    A polyhedron with twenty faces
  17. 17Regular icosahedron
    A polyhedron with twenty equilateral triangular faces
  18. 18Five Platonic solids
    Tetrahedron, cube, octahedron, dodecahedron, and icosahedron
  19. 19What makes a Platonic solid special?
    All faces are congruent regular polygons, and the same number of faces meet at each vertex
  20. 20Cylinder
    A solid with two parallel circular bases connected by a curved surface
  21. 21Cone
    A solid with a circular base that tapers smoothly to an apex
  22. 22Sphere
    The set of all points in 3D space at a given distance (radius) from a center point
  23. 23The surface of a sphere
    A sphere (the term can refer to both the surface and the enclosed ball)
  24. 24Ball
    The solid region bounded by a sphere (includes the interior)
  25. 25Volume
    The amount of three-dimensional space enclosed by a closed surface
  26. 26Surface area
    The total area of all the surfaces that bound a solid
  27. 27Volume formula for a cube
    V = s³, where s is the side length
  28. 28If a cube has side length 4, what is its volume?
    64 (V = 4³)
  29. 29Surface area formula for a cube
    SA = 6s², where s is the side length
  30. 30If a cube has side length 3, what is its surface area?
    54 (SA = 6 × 3²)

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