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Volume of a Hexagonal Prism

Volume of a Hexagonal Prism
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2016-06-23 22:48
PolygonSolid GeometryGeometric ConstructionSlider Animation
In collections Geo&Alg:Area Volume Pythagorean Th. CCSS G-GMD Geometric Measurement and Dimension
This GeoGebra example constructs a dynamic hexagonal prism whose height can be adjusted, demonstrating how to calculate the volume of a hexagonal prism. The core mathematical concept is the volume formula for prisms (base area × height), including the area calculation of a regular hexagon. The construction uses commands such as Circle, Segment, Intersect, Polygon, Prism, PointIn, Volume, and Slider to create the base hexagon, generate the prism, and update the volume in real time as the height changes. Text and Textfield objects display the computed values. This resource is suitable for middle or high school geometry classes, helping students understand the volume formula, explore the relationship between dimensions and volume, and develop spatial reasoning through interactive manipulation.

GeoGebra Commands & Parameters

  1. Circle(center, B, xOyPlane) → c
  2. Segment(center, B) → f
  3. Circle(B, f) → d
  4. Intersect(d, c) → C, D, ,
  5. Circle(D, f, xOyPlane) → e
  6. Circle(C, f, xOyPlane) → g
  7. Intersect(e, c) → E, F, ,
  8. Intersect(g, c) → G, H, ,
  9. Circle(G, f, xOyPlane) → h
  10. Intersect(h, c) → I, J, ,
  11. Polygon(B, D, F, I, G, C) → poly1, b, d_1, f_1, i, g_1, c_1
  12. Plane(L, A, K) → a
  13. Mirror(poly1, a) → hexagon
  14. Prism(hexagon, B) → HexPrism, M, face6, face2, CrossSection, edge1, edge2, edge3, edge4, edge5, edge6, edgeBM, N, edgeMN, edgeNO, edgeOP, edgePQ, edgeBQ, O, P, Q, face1, face3, face4, face5
  15. PointIn(CrossSection) → PointfaceBMNOPQ
  16. Volume(HexPrism) → volumej
  17. Point(HexPrism) → Pointj
  18. PointIn(CrossSection) → PointCrossSection
  19. PointIn(hexagon) → Pointpoly1'
  20. Text(PrismHeight, (x(B) + 0.2, y(B) + 0.5)) → text1
  21. Plane(R, a) → j
  22. Plane(S, a) → k
  23. Plane(T, a) → l
  24. Plane(U, a) → m
  25. Plane(V, a) → n
  26. Midpoint(edgeBQ) → W
  27. Segment(center, W) → p
  28. Angle(B, W, center, xOyPlane) → α
  29. Textfield(calc) → Calculator
  30. Segment(B, W) → q