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Prism Volume Calculation by Will Wassell

Prism Volume Calculation by Will Wassell
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2016-03-10 19:45
Solid GeometryGeometric Construction
This example demonstrates how to calculate the volume of a prism. It involves core mathematical concepts like volume formulas, polygon area, and spatial geometry. Constructed using commands such as Intersect, Point, Polygon, Prism, and Cylinder, with objects like faces, edges, and text to illustrate the calculation process. Suitable for high school solid geometry teaching or self-study to understand volume calculation principles.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(zAxis) → H
  6. Prism(poly1, H) → e, E, edgeBE, edgeCF, edgeDG, edgeEH, edgeEF, edgeFG, edgeGH, F, G, faceABEH, faceBCFE, faceCDGF, faceADGH, faceEFGH, edgeAH
  7. Point(xAxis) → I
  8. Prism(I, J, K, N) → f, L, edgeIK, edgeIN, edgeJL, edgeKM, edgeLN, edgeLM, edgeMN, M, faceIJK, faceIJLN, faceJKML, faceIKMN, faceLMN, edgeIJ, edgeJK
  9. Prism(O, P, Q, R, S, T, B_1) → g, U, faceRSZW, face3, face2, face4, edgeOP, edgePQ, edgeQR, edgeRS, edgeST, edgeOT, V, edge1, edgePU, edgeQV, edgeRW, edgeSZ, edge2, edge3, edgeUV, edgeVW, edgeWZ, W, edge5, edge4, Z, A_1, faceOPQRST, face1, facePQVU, faceQRWV
  10. Point(yAxis) → C_1
  11. Point(yAxis) → D_1
  12. Cylinder(C_1, D_1, 4) → h, k, p, i
  13. Point(yAxis) → I_1
  14. Polygon(G_1, H_1, I_1, J_1, E_1, F_1) → poly2, g_1, h_1, i_1, j_1, e_1, f_1
  15. Prism(poly2, l) → m, Q_1, face13, face12, face14, face18, edge20, edge21, edge22, edge23, edge18, edge19, R_1, edge24, edge26, edge27, edge28, edge29, edge25, S_1, T_1, U_1, V_1, face15, face16, face17