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Volume Calculation of Pyramid (Method I)

Volume Calculation of Pyramid (Method I)
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2020-07-22 15:37
Solid GeometryTransformationGeometric Construction
This example demonstrates how to calculate the volume of a pyramid using geometric construction. Key concepts include the volume formula of a pyramid and geometric transformations. Using GeoGebra commands such as Point, Cube, Net, Polygon, Pyramid, etc., the construction process of the pyramid is visually demonstrated. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Point(Circle[A, Distance[O, A], Segment[O, A]]) → B
  2. Cube(O, A, B) → b, C, faceBCGF, faceDEFG, edgeCO, edgeAO, edgeAB, edgeBC, edgeDO, edgeCG, edgeDG, edgeDE, D, edgeAE, edgeEF, edgeBF, edgeFG, E, F, G, faceABCO, faceCGDO, faceAEDO, faceABFE
  3. Net(b, Fold) → d, H, R, S, T, U, V, faceHIJK, faceHKML, faceHIRQ, faceIJTS, faceJKVU, I, faceLMNP, edgeHK, edgeHI, edgeIJ, edgeJK, edgeKM, edgeLM, edgeHL, edgeHQ, edgeQR, J, edgeIR, edgeIS, edgeST, edgeJT, edgeJU, edgeUV, edgeKV, edgeMN, edgeNP, edgeLP, K, L, M, N, P, Q
  4. Polygon(N, P, L, M) → q1, n, p, l, m
  5. Pyramid(q1, Size / 2) → e, W, faceNPW, faceLPW, faceLMW, faceMNW, edgeNW, edgePW, edgeLW, edgeMW
  6. Polygon(M, L, O, K) → q2, m_1, l_1, o, k
  7. Pyramid(q2, Size / 2) → f, Z, faceLMZ, faceLOZ, faceKOZ, faceKMZ, edgeMZ, edgeLZ, edgeOZ, edgeKZ
  8. Polygon(O, Q, R, I) → q3, o_1, q, r, i
  9. Pyramid(q3, Size / 2) → g, A_1, face2, face4, face3, face1, edge1, edge3, edge4, edge2
  10. Polygon(I, B, K, O) → q4, i_1, b_1, k_1, o_2
  11. Pyramid(q4, Size / 2) → h, B_1, face7, face8, face6, face5, edge7, edge6, edge8, edge5
  12. Polygon(I, S, T, B) → q5, i_2, s, t, b_2
  13. Pyramid(q5, Size / 2) → j, C_1, face11, face12, face10, face9, edge10, edge11, edge12, edge9
  14. Polygon(B, U, V, K) → q6, b_3, u, v, k_2
  15. Pyramid(q6, Size / 2) → w, D_1, face14, face16, face15, face13, edge13, edge15, edge16, edge14