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Prism Volume with Fixed Base Area

Prism Volume with Fixed Base Area
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2016-06-22 23:50
Solid GeometryGeometric Construction
This example demonstrates how the volume of prisms changes with a fixed base area. It involves core concepts like prism volume formulas, constant base area, and solid geometry. Constructed using commands such as Point, Segment, Polygon, Prism, and Volume, with Slider for dynamic adjustments. Suitable for high school solid geometry instruction to understand the relationship between volume and base area.

GeoGebra Commands & Parameters

  1. Point(Circle[A, sqrt((4 * AreaBase / tan(60°)))]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 3) → reg3, g, h, i, C
  4. Point(Circle[A, AreaBase / sqrt(AreaBase)]) → D
  5. Segment(A, D) → j
  6. Polygon(A, D, 4) → reg4, k, l, m, n, E, F
  7. Point(Circle[A, sqrt((4 * AreaBase / sqrt(25 + (10 * sqrt(5)))))]) → G
  8. Segment(A, G) → p
  9. Polygon(A, G, 5) → reg5, q, r, s, t, a, H, I, J
  10. Point(Circle[A, sqrt(((2 * AreaBase)) / ((3 * sqrt(3))))]) → K
  11. Segment(A, K) → b
  12. Polygon(A, K, 6) → reg6, c, O, d, e, f_1, g_1, h_1, L, M, N
  13. Point(Circle[A, sqrt(AreaBase / (2 + (2 * sqrt(2))))]) → P
  14. Segment(A, P) → i_1
  15. Polygon(A, P, 8) → reg8, j_1, R, S, T, U, V, k_1, l_1, m_1, n_1, p_1, q_1, r_1, Q
  16. Prism(reg3, top) → TriPrism, W, edgetopW, edgeWZ, edgetopZ, Z, faceABWtop, faceBCZW, faceACZtop, facetopWZ, edgeAtop_1, edgeBW, edgeCZ
  17. Prism(reg4, top) → SqPrism, A_1, edge1, edge2, edge3, edge4, edge6, edge7, edge5, B_1, C_1, face1, face3, face4, face2, face5, edgeAtop_2
  18. Prism(reg5, top) → PentPrism, D_1, face11, edgeAtop_3, edge8, edge9, edge10, edge11, edge12, edge14, edge15, edge16, E_1, edge13, F_1, G_1, face6, face8, face9, face10, face7
  19. Prism(reg6, top) → HexPrism, H_1, face17, face13, face18, edgeAtop_4, edge17, edge18, edge19, edge20, edge21, edge22, I_1, edge24, edge25, edge26, edge27, edge23, J_1, K_1, L_1, face12, face14, face15, face16
  20. Prism(reg8, top) → OctPrism, M_1, face22, face23, face24, face25, face26, face20, face27, edgeAtop, edge28, edge29, N_1, edge30, edge31, edge32, edge33, edge34, edge35, edge37, edge38, edge39, edge40, O_1, edge41, edge42, edge36, P_1, Q_1, R_1, S_1, face19, face21
  21. Volume(OctPrism) → volumeOctPrism
  22. Point(OctPrism) → PointOctPrism_1
  23. Volume(HexPrism) → volumeHexPrism
  24. Point(HexPrism) → PointHexPrism_1
  25. Volume(TriPrism) → volumeTriPrism
  26. Point(TriPrism) → PointTriPrism
  27. Volume(SqPrism) → volumeSqPrism
  28. Point(SqPrism) → PointSqPrism
  29. Volume(HexPrism) → o
  30. Point(HexPrism) → PointHexPrism
  31. Volume(OctPrism) → u
  32. Point(OctPrism) → PointOctPrism
  33. Volume(PentPrism) → volumePentPrism
  34. Point(PentPrism) → PointPentPrism_1
  35. Volume(PentPrism) → v
  36. Point(PentPrism) → PointPentPrism