Volume of a Rectangular Prism by Shawn

Volume of a Rectangular Prism by Shawn
Loading the math board and drawing, please wait…
2014-08-09 10:04
This example demonstrates how to construct a rectangular prism using GeoGebra and calculate its volume. Key math concepts include the dimensions (length, width, height) and the volume formula V = length × width × height. GeoGebra commands/objects used in the construction are Point, Segment, Rotate, Angle, Polygon, and Distance. Suitable for middle school students and above to learn about solid geometry volume calculation and spatial visualization skills.

GeoGebra Commands & Parameters

  1. Point(Circle[A, abs(Length)]) → B
  2. Segment(A, B) → a
  3. Point(Circle[A, abs(Height)]) → C
  4. Segment(A, C) → b
  5. Rotate(C, α, A) → C'
  6. Angle(C, A, C') → β
  7. Segment(A, C') → c
  8. Point(Circle[B, abs(Height)]) → D
  9. Segment(B, D) → d
  10. Rotate(D, α, B) → D'
  11. Angle(D, B, D') → γ
  12. Segment(D', B) → e
  13. Segment(C', D') → f
  14. Point(Circle[C', abs(Width)]) → E
  15. Segment(C', E) → g
  16. Rotate(E, δ, C') → E'
  17. Angle(E, C', E') → ε
  18. Segment(C', E') → h
  19. Point(Circle[A, abs(Width)]) → F
  20. Segment(A, F) → i
  21. Point(Circle[D', abs(Width)]) → G
  22. Segment(D', G) → j
  23. Point(Circle[B, abs(Width)]) → H
  24. Segment(B, H) → k
  25. Rotate(G, δ, D') → G'
  26. Angle(G, D', G') → ζ
  27. Rotate(H, δ, B) → H'
  28. Angle(H, B, H') → η
  29. Rotate(F, δ, A) → F'
  30. Angle(F, A, F') → θ
  31. Segment(D', G') → l
  32. Segment(A, F') → m
  33. Segment(B, H') → n
  34. Segment(E', G') → p
  35. Segment(G', H') → q
  36. Segment(F', E') → r
  37. Segment(F', H') → s
  38. Polygon(C', E', F', A) → poly1, c', e', f', a_2
  39. Polygon(E', G', H', F') → poly2, e'_1, g', h', f'_1
  40. Polygon(C', E', G', D') → poly3, c'_1, e'_2, g'_1, d'
  41. Polygon(C', D', B, A) → poly4, c'_2, d'_1, b_2, a_3
  42. Polygon(A, F', H', B) → poly5, a_4, f'_2, h'_1, b_3
  43. Polygon(D', G', H', B) → poly6, d'_2, g'_2, h'_2, b_4
  44. Distance(A, B) → AB
  45. Segment(C', E') → t

AI Drawing Prompt Reference

Draw a rectangular prism to demonstrate volume calculation. Start by constructing the base and sides, using points, segments, and rotations to form the base's length and width, then vertically construct the height. Rotate and connect segments to complete all faces of the prism. Finally, fill each face with different colored polygons and label the dimensions of length, width, and height to visually show the volume formula V = length × width × height.
The prompt above was compiled from the original drawing commands and is for reference only.