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Volume of Prisms by Will Wassell

Volume of Prisms by Will Wassell
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2016-03-10 19:43
Solid GeometryGeometric Construction
This example demonstrates the calculation of the volume of prisms. Key mathematical concepts include the definition of prisms, volume formulas, and their applications. Using GeoGebra commands such as Intersect, Point, Polygon, Prism, etc., the construction process of prisms is visually demonstrated. Suitable for middle school and above students to learn geometry and volume calculations.

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

AI Drawing Prompt Reference

Draw a prism by first determining the four vertices A, B, C, D of the base on the coordinate axes, then forming a quadrilateral with these points. Next, determine the center point H of the top face on the z-axis and construct the prism using the base and the top center point. Then, draw another prism with base vertices I, J, K, N and top center point L. After that, draw a third prism with base vertices O, P, Q, R, S, T and top center point U. Finally, draw a cylinder with base center points C1, D1 and height 4.
The prompt above was compiled from the original drawing commands and is for reference only.