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Volume of Composite Solid

Volume of Composite Solid
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2018-04-14 01:24
Solid GeometryCalculusParametric EquationGeometric Construction
This example demonstrates how to calculate the volume of a composite solid formed by a parallelogram prism and parametric curves. It involves core mathematical concepts such as volume computation, real numbers, parallelogram properties, parametric curves, and 3D shape understanding. The construction uses GeoGebra commands/objects like Textfield, Prism, Segment, and Polygon. Suitable for high school students learning complex geometric volume calculations and parametric equations applications.

GeoGebra Commands & Parameters

  1. Textfield(usertext) → InputBox1
  2. Prism(A1, B1, C1, D1, E1) → PrismA1, F1, edgeA1B1, edgeB1C1, edgeC1D1, edgeA1D1, edgeA1E1, edgeAB1, edgeBC1, edgeCD1, S1D2line, S1D1line, G1, edgeBC_1, edgeCE1, H1_1, faceA1B1C1D1, S2B1face, S1B2face, faceBCD1C1, faceA1D1CE1, faceABCE1
  3. Prism(F1, G1, I1, E1) → PrismB1, K1, edgeF1I1, edgeE1F1, edgeAG1, edgeBI1, edgeAE1, edgeAB_2, edgeBE1, J1, S1R2face, faceAE1F1G1, faceABI1G1, S1R1face, faceABE1, edgeF1G1, edgeG1I1
  4. Prism(A2, B2, C2, D2, E2) → PrismA2, F2, edgeA2B2, edgeB2C2, edgeC2D2, edgeA2D2, edgeA2E2, edgeAB2, edgeBC2, edgeCD2, edgeAE2, edgeAB_3, G2, edgeBC_2, edgeCE2, H2_1, faceA2B2C2D2, S1B1face, S2B2face, faceBCD2C2, faceA2D2CE2, S2B3face
  5. Prism(G2, H2_1, I2, J2, K2) → PrismB2, L2, edgeG2H2, edgeH2I2, edgeI2J2, S2D1line, edgeG2K2, edgeAH2, edgeBI2, edgeCJ2, edgeAK2, edgeAB_4, M2, edgeBC_3, edgeCK2, N2, faceG2H2I2J2, faceAH2G2K2, faceABI2H2, S2R2face, S2R3face, S2R1face
  6. Prism(A3, B3, C3, D3, E3) → PrismA3, F3, edgeA3B3, edgeB3C3, edgeC3D3, edgeA3D3, edgeA3E3, edgeAB3_1, edgeBC3, edgeCD3, edgeAE3, edgeAB_5, G3, edgeBC_4, edgeCE3, H3, faceA3B3C3D3, faceAB3A3E3, S3R3face, S3R1face, faceA3D3CE3, S3R2face
  7. Prism(J3, B3, F3, I3, K3) → PrismB3, L3, edgeB3J3, edgeB3F3, S3D1line, edgeI3J3, edgeJ3K3, edgeAB3, edgeBF3, edgeCI3, edgeAK3, edgeAB_6, M3, edgeBC_5, edgeCK3, N3, faceB3F3I3J3, faceAB3J3K3, faceABF3B3, S3B1face, S3B2face, S3B3face
  8. Prism(A5, B5, C5, D5, E5) → PrismA5, F5, edgeA5B5, edgeB5C5, edgeC5D5, edgeA5D5, edgeA5E5, edgeAB5, edgeBC5, edgeCD5, edgeAE5, S5D1line, G5, edgeBC_7, edgeCE5, H5, faceA5B5C5D5, S5R2face, S5R1face, faceBCD5C5, faceA5D5CE5, faceABCE5
  9. Prism(I5, J5, K5, L5, M5) → PrismB5, N5, edgeI5J5, edgeJ5K5, edgeK5L5, edgeI5L5, edgeI5M5, edgeAJ5, edgeBK5, edgeCL5, edgeAM5, edgeAB_7, O5, edgeBC_6, edgeCM5, P5, faceI5J5K5L5, S5B2face, S5B1face, faceBCL5K5, faceB5C5, S5B3face
  10. Prism(A4, B4, C4, D4, E4) → PrismA4, F4, edgeA4B4, edgeB4C4, edgeC4D4, edgeA4D4, edgeA4E4, edgeAB4, edgeBC4, edgeCD4, edgeAE4, edgeAB_8, G4, edgeBC_8, edgeCE4, H4, faceA4B4C4D4, S4B8face, S4B7face, faceBCD4C4, faceA4D4CE4, S4G2face
  11. Prism(E4, F4, J4, I4, K4) → PrismB4, L4, edgeE4F4, edgeF4J4, edgeI4J4, edgeE4I4, edgeE4K4, edgeAF4, edgeBJ4, edgeCI4, edgeAK4, edgeAB_{10}, M4, edgeBC_9, edgeCK4_1, N4, faceE4F4J4I4, S4B6face, S4B5face, faceBCI4J4, faceCI4E4K4, faceABCK4
  12. Prism(H4, G4, P4, O4, Q4) → PrismC4, R4, edgeG4H4, edgeG4P4, edgeO4P4, edgeH4O4, edgeH4Q4, edgeAG4, edgeBP4, edgeCO4, edgeAQ4, edgeAB_{11}, S4, edgeBC_{10}, edgeCQ4, T4, faceG4H4O4P4, faceAG4H4Q4, S4B4face, S4G1face, faceCO4H4Q4, faceABCQ4
  13. Prism(Q4, R4, L4, K4, U4) → PrismD4, V4, edgeQ4R4, edgeL4R4, edgeK4L4, edgeK4Q4, edgeQ4U4, edgeAR4, edgeBL4, edgeCK4, edgeAU4, edgeAB, W4, edgeBC, edgeCU4, X4, faceK4L4R4Q4, faceAR4Q4U4, S4B2face, S4B3face, faceCK4Q4U4, S4B1face
  14. Segment(J2, F2) → edgeJF2
  15. Segment(G3, I3) → lineGI3
  16. Segment(S4, M4) → lineSM4
  17. Segment(P4, J4) → linePJ4
  18. Polygon(S4, M4, J4, P4) → S4R1face, s4, m4, j4, p4
  19. Segment(K5, G5) → lineKG5
  20. Segment(J5, F5) → lineJF5
  21. Segment((-2.5, -2, 0), (-2.5, -2, 4)) → S1HeightMarker
  22. Segment((-0.95929, -3.28198, 0), Midpoint[P4, J4]) → S4Arrow1
  23. Segment((-2.5, -2.21887, 1), Midpoint[S4, P4]) → S4Arrow2
  24. Segment((-3.5, -1, 4), (-3.5, -1, 0)) → S5HeightMarker

AI Drawing Prompt Reference

Create a 3D composite solid formed by multiple prisms, starting with a parallelogram-based prism and adding several other prisms that stack or intersect. Include visible edges, vertices, and faces of the prisms, along with height markers and arrows indicating dimensions. The construction should show the prisms in a spatial arrangement, with some prisms sharing faces or edges. Add line segments to highlight specific edges and arrows to denote measurements. The overall scene should illustrate volume calculation of a composite solid, with a clear 3D perspective.
The prompt above was compiled from the original drawing commands and is for reference only.