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Measuring the Volume of a Rectangular Prism

Measuring the Volume of a Rectangular Prism
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2017-04-05 10:37
FunctionSequenceSolid Geometry
This example demonstrates how to calculate the volume of a rectangular prism by inputting its length, width, and height. Core math concepts include volume calculation formula (length×width×height), solid geometry, polynomial functions, multiplication, algebra, and addition. Key construction elements involve GeoGebra commands/objects like If, Prism, and Sequence. Suitable for high school students to learn and understand volume calculation methods and explore related mathematical concepts.

GeoGebra Commands & Parameters

  1. If(HS ≥ 12, Text[floor(HS / 12)], "") → Hint
  2. If(WS ≥ 12, Text[floor(WS / 12)], "") → Wint
  3. If(LS ≥ 12, Text[floor(LS / 12)], "") → Lint
  4. If((WS - (floor(WS / 12) * 12)) / 12 ≟ 0, "", FractionText[(WS - (floor(WS / 12) * 12)) / 12]) → Wfrac
  5. Prism(Polygon[A, B, D, C], E) → a, F, edgeBF, edgeDG, edgeCH, edgeEF, edgeFG, edgeGH, edgeEH, G, H, faceABFE, faceBDGF, faceCDGH, faceACHE, faceEFGH, edgeAE
  6. Sequence(Segment[(i, 0, height), (i, width, height)], i, 0, floor(length)) → list1
  7. Sequence(Segment[(i, 0, 0), (i, 0, height)], i, 0, floor(length)) → list2
  8. Sequence(Segment[(length, i, 0), (length, i, height)], i, 0, floor(width)) → list3
  9. Sequence(Segment[(0, 0, i), (length, 0, i)], i, 0, floor(height)) → list4
  10. Sequence(Segment[(length, 0, i), (length, width, i)], i, 0, floor(height)) → list5
  11. Sequence(Segment[(0, i, height), (length, i, height)], i, 0, floor(width)) → list6
  12. Sequence(Segment[(0, 0, i), (0, width, i)], i, 0, floor(height)) → list7
  13. Sequence(Segment[(0, width, i), (length, width, i)], i, 0, floor(height)) → list8
  14. Sequence(Segment[(0, i, 0), (0, i, height)], i, 0, floor(width)) → list9
  15. Sequence(Segment[(i, width, 0), (i, width, height)], i, 0, floor(length)) → list10
  16. Sequence(Segment[(0, i, 0), (length, i, 0)], i, 0, floor(width)) → list11
  17. Sequence(Segment[(i, width, 0), (i, 0, 0)], i, 0, floor(length)) → list12
  18. If(b, 12, 1) → skips

AI Drawing Prompt Reference

Draw a rectangular prism and show the volume calculation process. First, use different colored lines to draw the 12 edges of the prism, labeling length, width, and height. Then, construct three faces of the prism using these edges and fill them with colors. Next, draw dashed lines inside the prism parallel to each face to form an internal grid. Finally, next to the prism, use a formula and text to explain the volume calculation formula: length×width×height, and display the input values and calculation result dynamically.
The prompt above was compiled from the original drawing commands and is for reference only.