MathPlotAI Logo MathPlotAI

Unfolding a Cube by Arthur Lee

Unfolding a Cube by Arthur Lee
Loading the math board and drawing, please wait…
2014-11-27 20:50
Solid GeometryGeometric Construction
In collections Dissecting a cube into equal parts 3D Geometry & Cross Sections Surface Area & Volume Surface Area & Volume Surface Area and Volume Connolly Geometry Volume
This example demonstrates how to cut a cube into 6 congruent pyramids to explore the volume of each pyramid. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Point, Cube, Midpoint, Pyramid, Circle, Angle, Rotate, Line, OrthogonalPlane, Mirror, one can intuitively understand geometric transformations and volume calculations. Suitable for middle school and above students to learn solid geometry and volume calculation.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Midpoint(D, F) → I
  6. Pyramid(faceABCD, I) → b, faceADI, faceABI_1, faceBCI, faceCDI, edgeDI, edgeAI_1, edgeBI_1, edgeCI
  7. Circle(edgeAB, F) → c
  8. Point(c) → J
  9. Angle(F, B, J) → α
  10. Pyramid(faceABFE, I) → d, faceABI, faceAEI, faceEFI, faceBFI, edgeBI, edgeAI, edgeEI, edgeFI
  11. Rotate(d, α, edgeAB) → d'
  12. Rotate(d', 90*°, zAxis) → d''
  13. Rotate(d'', 90*°, zAxis) → d'''
  14. Rotate(d''', 90*°, zAxis) → e
  15. Line(B, J) → f
  16. Midpoint(B, J) → K
  17. OrthogonalPlane(K, f) → g
  18. Mirror(b, g) → b'