MathPlotAI Logo MathPlotAI

Volume Comparison: Prism & Pyramid with Same Base & Height

Volume Comparison: Prism & Pyramid with Same Base & Height
Loading the math board and drawing, please wait…
2016-06-23 23:28
Solid GeometryGeometric Construction
This example demonstrates the volume comparison between a prism and a pyramid with identical base area and height. Key math concepts include volume formulas, geometric properties, and spatial visualization. It utilizes GeoGebra commands like Circle, Segment, Intersect, Polygon, Plane, Mirror, Prism, Pyramid, etc., to construct the models. Suitable for high school students learning solid geometry to intuitively understand volume calculations and comparisons.

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. Pyramid(hexagon, center) → Pyramid, face7, edge10, edge11, edge12, face9, face10, face11, face12, face8, edge7, edge8, edge9
  31. Volume(Pyramid) → volumePyra
  32. Point(Pyramid) → PointPyra
  33. Segment(B, W) → q