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Volume of Pyramid and Cube 1

Volume of Pyramid and Cube 1
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2017-12-27 21:59
Solid GeometryCalculusGeometric Construction
In collections Mathematics Form 2
This example demonstrates the calculation and comparison of volumes for pyramids and cubes. It involves core mathematical concepts such as volume formulas, geometric properties, and integral calculus. Construction highlights include using GeoGebra commands like If, Line, Vector, Midpoint, Translate, Rotate, SelectedIndex to build the shapes and compute volumes. Suitable for high school students and math enthusiasts studying solid geometry and calculus.

GeoGebra Commands & Parameters

  1. If(2 < e ≤ 3, e - 2, If[e ≤ 2, 0, 1]) → h_2
  2. If(1 < e < 2, e - 1, If[e ≤ 1, 0, 1]) → h_1
  3. If(e < 1, e, 1) → h_0
  4. Line(A, xAxis) → l
  5. Vector(A, B) → w
  6. Line(D, yAxis) → n
  7. Midpoint(B, D) → L
  8. Vector(L, D) → u
  9. Translate((x(A) - (3 * Bs / 2), y(A) + Bs / 2, z(A) + Bs), Vector[(h_0 * u)]) → H_1
  10. Vector(L, A) → v
  11. Translate((x(A) - Bs / 2, y(A) + Bs / 2, z(A) + Bs), Vector[(h_0 * u)]) → H_0
  12. Rotate(Translate[Rotate[Pyramid[Polygon[D, C, (x(A) - (2 * Bs), y(A) + Bs), (x(A) - (2 * Bs), y(A))], H_1], ((h_1 * 90))°, l], Vector[(h_1 * w)]], (((-h_2) * 90))°, n) → p_3
  13. Translate((x(A) + Bs / 2, y(A) + Bs / 2, z(A) + Bs), Vector[(h_0 * v)]) → H_2
  14. Rotate(Pyramid[Polygon[A, B, C, D], H_0], 0°, xAxis) → p_1
  15. If(3 < e ≤ 4, e - 3, 0) → h_3
  16. Line(A, yAxis) → m
  17. Rotate(Pyramid[Polygon[A, (x(A) + Bs, y(A)), (x(A) + Bs, y(A) + Bs), B], H_2], (((-h_3) * 90))°, m) → p_2
  18. SelectedIndex(Bahasa) → nn
  19. If(nn ≟ 1, "Animation", "Animasi") → Tex1
  20. If(nn ≟ 1, "Stop", "Berhenti") → Tex2
  21. If(nn ≟ 1, "Height of pyramid = ", "Tinggi piramid = ") → Tex3
  22. If(nn ≟ 1, If[Bs ≟ 1, " unit", " units"], " unit") → UTex
  23. If(nn ≟ 1, "Base dimensions of pyramid = ", "Dimensi tapak piramid = ") → Tex4

AI Drawing Prompt Reference

Draw a cube and a pyramid sharing the same base, demonstrating volume calculation and comparison. The pyramid's apex is vertically above the base center. Use distinct colors for each shape and label their volume formulas. Adjust the pyramid's height with a slider while keeping the cube's height fixed. Display volume calculations and geometric properties beside the shapes for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.