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Volume of Prisms by Catherine

Volume of Prisms by Catherine
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2018-01-03 21:59
Solid GeometryGeometric Construction
This example demonstrates the calculation of the volume of prisms. Key concepts include the definition of prisms, volume formulas, and their applications. Using GeoGebra commands such as Point, Polygon, Vector, Translate, etc., users can dynamically adjust the dimensions of the prism to intuitively understand volume changes. Suitable for middle school and above students learning geometry and volume calculations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 2]) → X
  2. Polygon(A, X, C, D) → poly1, b_6, b_5, c, h_3
  3. Vector(E, F) → u
  4. Translate(A, v) → A'
  5. Translate(X, v) → B'
  6. Translate(C, v) → C'
  7. Translate(D, v) → D'
  8. Polygon(A', B', C', D') → poly1', a', b', c', d'
  9. Polygon(B', X, A, A') → poly2, b'_1, b_1, a_1, a'_1
  10. Intersect(c', b') → G
  11. Intersect(c, b_5) → H
  12. Polygon(B', G, H, X) → poly3, b'_2, g, h_2, b_2
  13. Intersect(h_3, c) → I
  14. Intersect(d', c') → J
  15. Polygon(G, H, I, J) → poly4, g_1, h_1, i, j
  16. Polygon(J, I, A, A') → poly5, j_1, i_1, a_2, a'_2
  17. Point(Circle[K, 4]) → Y
  18. Polygon(K, Y, M, N) → poly6, b_7, l, m, h_4
  19. Point(xAxis) → O
  20. Vector(O, P) → w
  21. Translate(K, z) → K'
  22. Translate(Y, z) → L'
  23. Translate(M, z) → M'
  24. Translate(N, z) → N'
  25. Polygon(K', L', M', N') → poly6', k', l', m', n'
  26. Polygon(L', Y, K, K') → poly7, l'_1, l_1, k_1, k'_1
  27. Intersect(m', l') → Q
  28. Intersect(m, l) → R
  29. Polygon(L', Q, R, Y) → poly8, l'_2, q, r, l_2
  30. Point(m') → S
  31. Intersect(h_4, m) → T
  32. Polygon(R, Q, S, T) → poly9, r_1, q_1, s, t
  33. Polygon(T, R, Y, K) → poly10, t_1, r_2, l_3, k_2
  34. Polygon(K', S, T, K) → poly11, k'_2, s_1, t_2, k_3
  35. Point(Circle[U, 4.47213595499958]) → Z
  36. Polygon(U, Z, W) → poly12, w_1, h, b
  37. Point(xAxis) → Z_1
  38. Vector(Z_1, A_1) → p
  39. Translate(U, z_1) → U'
  40. Translate(Z, z_1) → V'
  41. Translate(W, z_1) → W'
  42. Polygon(U', V', W') → poly12', w', u', v'
  43. Intersect(b, h) → B_1
  44. Intersect(v', u') → C_1
  45. Polygon(U', U, B_1, C_1) → poly13, u'_1, u_2, b_3, c_1
  46. Polygon(U', U, Z, V') → poly14, u'_2, u_3, v_2, v'_1
  47. Polygon(V', Z, B_1, C_1) → poly15, v'_2, v_3, b_4, c_2
  48. Polygon(R, Q, S, T) → poly16, r_3, q_2, s_2, t_3