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Volume Calculation by huỳnh văn đèo

Volume Calculation by huỳnh văn đèo
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2015-02-07 12:08
Solid GeometryCalculusIntegral
This example demonstrates how to calculate the volume of different shapes using geometric construction and integration. It covers key concepts such as volume, fractions, median value, pyramid, straight lines, and histograms. Using GeoGebra commands like Sequence, Segment, and Sum, complex geometric shapes can be constructed and dynamically demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(a + Δx / 2 + (i * Δx), c + Δy / 2 + (j * Δy)), i, 0, m - 1], j, 0, n - 1) → ptos
  2. Sequence(c + (i * Δy), i, c, n) → particaocd
  3. Sequence((a + (i * Δx), c), i, 0, m) → particaopontosab
  4. Sequence((a, c + (i * Δy)), i, 0, n) → particaopontoscd
  5. Segment((b, 0), (b, d)) → lado1
  6. Segment((0, d), (b, d)) → lado2
  7. Sequence((b, c + (i * Δy)), i, 0, n) → pontoslado1
  8. Sequence((a + (i * Δx), d), i, 0, m) → pontoslado2
  9. Sequence(Segment[Element[particaopontosab, i], Element[pontoslado2, i]], i, 1, m + 1) → segvertical
  10. Sequence(Sequence[Polygon[(a + ((i - 1) * Δx), c + ((j - 1) * Δy)), (a + (i * Δx), c + ((j - 1) * Δy)), 4], i, 1, n], j, 1, n) → poligonos
  11. Sum(Sequence[Sum[Sequence[Element[matriz1, i, j], j, 1, m]], i, 1, n]) → somaf
  12. Sequence(Segment[Element[particaopontoscd, i], Element[pontoslado1, i]], i, 1, n + 1) → seghorizontal
  13. Sequence(a + (i * Δx), i, a, m) → particaoab
  14. Sequence(Sequence[(a + Δx / 2 + (i * Δx) + (Δx / 2 * random()), c + Δy / 2 + (j * Δy) + (Δy / 2 * random())), i, 0, m - 1], j, 0, n - 1) → ptosaleat
  15. Sequence(Sequence[Intersect[Element[segvertical, i], Element[seghorizontal, j]], i, 1, m + 1], j, 1, n + 1) → pontos
  16. Sequence(Polygon[Element[pontos, 1, j], Element[pontos, 1, j + 1], Element[pontos, 2, j + 1], Element[pontos, 2, j]], j, 1, m) → base1
  17. Sequence(Sequence[Polygon[Element[pontos, i, j], Element[pontos, i, j + 1], Element[pontos, i + 1, j + 1], Element[pontos, i + 1, j]], j, 1, m], i, 1, n) → base
  18. Sequence(Sequence[Prism[Element[base, i, j], Element[matriz1, i, j]], j, 1, m + 1], i, 1, n + 1) → prismas
  19. Sum(Sequence[Element[matriz1, 1, j], j, 1, m]) → e
  20. Sum(Sequence[Sum[Sequence[Element[matriz2, i, j], j, 1, m]], i, 1, n]) → somaaleatf
  21. Sequence(Sequence[Prism[Element[base, i, j], Element[matriz2, i, j]], j, 1, m + 1], i, 1, n + 1) → prismasaleat
  22. Sequence(Sequence[Text["P_" + (i) + (("_" * j)), Element[ptos, i, j] + 0.1], j, 1, m], i, 1, n) → textopts
  23. Sequence(Sequence[Text["P_" + (i) + (("_" * j)), Element[ptosaleat, i, j] + 0.1], j, 1, m], i, 1, n) → textoptosaleat

AI Drawing Prompt Reference

Draw a 3D shape composed of multiple upright rectangles, with their bases aligned horizontally and heights varying randomly according to a given matrix. First, draw horizontal and vertical lines to divide the space, then construct rectangles based on these lines, and finally stack them to form the 3D shape.
The prompt above was compiled from the original drawing commands and is for reference only.