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Surface Area Calculation Demo

Surface Area Calculation Demo
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2019-11-08 01:00
VectorFunctionSolid GeometryCalculusGeometric Construction
This example demonstrates how to construct 3D solids (like prisms) and calculate their surface area using GeoGebra. Key math concepts include area, multiplication, unit circle, definite integral, and solid geometry. Construction highlights the use of commands like Ray, Prism, Net, Sequence, Translate, Vector, Mirror, along with objects like LENGTH, WIDTH, HEIGHT, and faces. Suitable for high school solid geometry teaching and introductory mathematical modeling.

GeoGebra Commands & Parameters

  1. Ray((0, 0, 0), (1, 0, 0)) → f
  2. Ray((0, 0, 0), (0, 1, 0)) → g
  3. Ray((0, 0, 0), (0, 0, 1)) → h
  4. Prism(E, A, D, B, C) → d, F, edgeAE, edgeAD, edgeBD, edgeBE, edgeCE, edgeAF, edgeDG, edgeBH, edgeCF, edgeFG, G, edgeGH, edgeCH, H, faceADBE, faceAECF, faceADGF, faceBDGH, faceBECH, faceCFGH
  5. Net(d, openclose) → i, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  6. Sequence(Segment[(i, 0, 0), (i, WIDTH, 0)], i, 1, LENGTH - 1, 1) → L_1
  7. Translate(L_1, Vector[A, F]) → L_2
  8. Sequence(Segment[(0, i + 1, 0), (LENGTH, i + 1, 0)], i, 0, WIDTH - 2) → L_3
  9. Translate(L_3, Vector[A, F]) → L_4
  10. Vector(M, V) → u
  11. Sequence((x(M) + i, y(M), z(M)), i, 1, LENGTH - 1, 1) → L_5
  12. Translate(L_5, u) → L_6
  13. Sequence(Segment[Element[L_5, i], Element[L_6, i]], i, 1, LENGTH - 1) → L_7
  14. Sequence((x(M), y(M) + (i * y(u) / WIDTH), z(M) + (i * z(u) / WIDTH)), i, 1, WIDTH - 1, 1) → L_8
  15. Vector(V, U) → v
  16. Translate(L_8, v) → L_9
  17. Sequence(Segment[Element[L_8, i], Element[L_9, i]], i, 1, WIDTH - 1) → L_{10}
  18. Vector(A, O) → w
  19. Sequence((x(A) + (i * x(w) / HEIGHT), y(A), z(A) + (i * z(w) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{11}
  20. Vector(O, P) → l
  21. Translate(L_{11}, l) → L_{12}
  22. Sequence(Segment[Element[L_{11}, i], Element[L_{12}, i]], i, 1, HEIGHT - 1) → L_{13}
  23. Sequence((x(O), y(O) + (i * y(l) / WIDTH), z(O) + (i * z(l) / WIDTH)), i, 1, WIDTH - 1, 1) → L_{14}
  24. Translate(L_{14}, Vector[(-w)]) → L_{15}
  25. Sequence(Segment[Element[L_{14}, i], Element[L_{15}, i]], i, 1, WIDTH - 1) → L_{16}
  26. Mirror(L_{13}, k) → L_{17}
  27. Mirror(L_{16}, k) → L_{18}
  28. Vector(D, Q) → m
  29. Sequence((x(B) + (i * x(v) / LENGTH), y(B), z(B)), i, 1, LENGTH - 1, 1) → L_{19}
  30. Translate(L_{19}, m) → L_{20}
  31. Sequence(Segment[Element[L_{19}, i], Element[L_{20}, i]], i, 1, LENGTH - 1) → L_{21}
  32. Sequence((x(B), y(B) + (i * y(m) / HEIGHT), z(B) + (i * z(M) / HEIGHT)), i, 1, HEIGHT - 1, 1) → L_{22}
  33. Translate(L_{22}, v) → L_{23}
  34. Sequence(Segment[Element[L_{22}, i], Element[L_{23}, i]], i, 1, HEIGHT - 1) → L_{24}
  35. Mirror(L_{21}, n) → L_{25}
  36. Mirror(L_{24}, n) → L_{26}