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Measuring Volume 3

Measuring Volume 3
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2016-05-30 17:19
FunctionSolid GeometryCalculusGeometric Construction
In collections Geo&Alg:Area Volume Pythagorean Th.
This example demonstrates how to measure the volume of 3D shapes by constructing a regular triangle and a parabola, involving core concepts like definite integrals, solid geometry, and function graphing. Key GeoGebra commands used include Point, Cube, and Translate for creating points, cubes, and transformations. Suitable for high school students learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Point(Circle[J, Distance[I, J], Segment[I, J]]) → K
  3. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  4. Point(Circle[H_1, Distance[G_1, H_1], Segment[G_1, H_1]]) → I_1
  5. Cube(G_1, H_1, I_1) → e_1, J_1, face11, facez, edge13, edge12, edge15, edge17, edge14, edge19, edge21, edge20, K_1, edge16, edge22, edge18, edge23, L_1, M_1, N_1, face7, face9, facey, facex
  6. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (2, 1)]) → f
  7. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 0)]) → g
  8. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1, 1)]) → h
  9. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1)]) → e
  10. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1)]) → e'
  11. Translate(facex, Vector[(0, 0, 0), (0, -1, 0)]) → facex010
  12. Translate(facey, Vector[(0, 0), (1, 0, 0)]) → facey100
  13. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 0)]) → a
  14. Translate(facez, Vector[(0, 0, 0), (0, -1, 0)]) → facez010
  15. Translate(facey, Vector[(0, 0, 1)]) → facey001
  16. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 0, 1)]) → b
  17. Translate(facey, Vector[(0, -1, 0)]) → facey010
  18. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, -1)]) → c
  19. Translate(facex, Vector[(0, -3, 0)]) → facex030
  20. Translate(facex, Vector[(1, 0, 0)]) → facex100
  21. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(3, 1)]) → k
  22. Translate(facez, Vector[(0, -3, 0)]) → facez030
  23. Translate(facex, Vector[(0, 0, 1)]) → facex001
  24. Translate(facez, Vector[(1, 0, 0)]) → facez100
  25. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 1, 1)]) → q
  26. Translate(facez, Vector[(0, 0, 1)]) → facez001
  27. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 1, 2)]) → u
  28. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (2, 1)]) → f'
  29. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 0)]) → a'
  30. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 0)]) → g'
  31. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(3, 1)]) → k'
  32. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, -1)]) → c'
  33. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1, 1)]) → h'
  34. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 0, 1)]) → b'
  35. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 1, 1)]) → q'
  36. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 1, 2)]) → u'
  37. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[D]) → b_1
  38. Translate(Prism[Polygon[(-5, 2, 0), (-5, -1, 0), (-4, -1, 0), (-4, 0, 0), (-3, 0, 0), (-3, 1, 0), (-2, 1, 0), (-2, 2, 0)], (-5, 2, 1)], Vector[(0, 0)]) → d
  39. Translate(Prism[Polygon[(-5, 2, 1), (-5, 0, 1), (-4, 0, 1), (-4, 1, 1), (-3, 1, 1), (-3, 2, 1)], 1], Vector[(0, 0)]) → i
  40. Translate(Prism[Polygon[(-5, 2, 2), (-5, 1, 2), (-4, 1, 2), (-4, 2, 2)], 1], Vector[(0, 0)]) → j
  41. Translate(Prism[Polygon[(-5, 2, 0), (-5, -1, 0), (-4, -1, 0), (-4, 0, 0), (-3, 0, 0), (-3, 1, 0), (-2, 1, 0), (-2, 2, 0)], (-5, 2, 1)], Vector[(0, 0)]) → l
  42. Translate(Prism[Polygon[(-5, 2, 1), (-5, 0, 1), (-4, 0, 1), (-4, 1, 1), (-3, 1, 1), (-3, 2, 1)], 1], Vector[(0, 0)]) → m
  43. Translate(Prism[Polygon[(-5, 2, 2), (-5, 1, 2), (-4, 1, 2), (-4, 2, 2)], 1], Vector[(0, 0)]) → n
  44. Translate(Polygon[(-5, 0, 0), (-4, 0, 0), (-4, 0, 1), (-5, 0, 1)], Vector[(0, 0)]) → poly1
  45. Translate(Polygon[(-5, 1, 0), (-3, 1, 0), (-3, 1, 1), (-4, 1, 1), (-4, 1, 2), (-5, 1, 2)], Vector[(0, 0)]) → poly2
  46. Translate(Polygon[(-3, 1, 0), (-3, 2, 0), (-3, 2, 1), (-3, 1, 1)], Vector[(0, 0)]) → poly3
  47. Translate(Polygon[(-4, 0, 0), (-4, 2, 0), (-4, 2, 2), (-4, 1, 2), (-4, 1, 1), (-4, 0, 1)], Vector[(0, 0)]) → poly4