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Surface Area and Volume of Prisms and Cylinders by Jose Arturo Gomez Velasquez

Surface Area and Volume of Prisms and Cylinders by Jose Arturo Gomez Velasquez
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2015-02-02 09:14
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area-Volumen-Algebra-inequalities-Trigonometric
This example demonstrates the calculation of the volume of prisms and cylinders. Key concepts include the product of the base area and height. Using GeoGebra commands such as Intersect, Point, Prism, Line, Cylinder, Circle, etc., the geometric shapes of prisms and cylinders can be constructed. Suitable for middle and high school students learning geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Point(Circle[B, Distance[C, B], Segment[C, B]]) → I
  5. Point(yAxis) → D
  6. Point(yAxis) → E
  7. Point(xAxis) → F
  8. Point(zAxis) → K
  9. Prism(A, F, C, E, K) → a, G, edgeAF, edgeCF, edgeCE, edgeAE, edgeAK, edgeFG, edgeCH, edgeEJ, edgeGK, edgeGH, H, edgeHJ, edgeJK, J, faceAECF, faceAFGK, faceCFGH, faceCEJH, faceAEJK, faceGHJK
  10. Line(I, zAxis) → b
  11. Cylinder(L, I, 0.5) → c, d, e, f
  12. Cylinder(I, L, 2) → g, h, k, i
  13. Circle(I, 0.5, xOyPlane) → p
  14. Cylinder(p, 2) → m, r, n
  15. Point(yAxis) → M
  16. Line(M, xAxis) → j
  17. Point(xAxis) → O
  18. Point(xAxis) → P
  19. Point(j) → Q
  20. Polygon(N, Q, O) → poly1, o, n_1, q
  21. Prism(poly1, 1) → s, U, edgeOW, edgeUV, edgeVW, edgeUW, V, W, faceNQVU, faceOQVW, faceNOWU, faceUVW, edgeNU, edgeQV
  22. Point(yAxis) → R
  23. Line(D, xAxis) → l
  24. Line(R, xAxis) → t
  25. Point(t) → A_1
  26. Point(t) → B_1
  27. Polygon(A_1, Z, S, T, B_1) → poly3, a_1, z_1, s_1, t_1, b_1
  28. Line(S, b) → c_1
  29. Line(Z, b) → d_1
  30. Line(A_1, c_1) → e_1
  31. Line(B_1, c_1) → f_1
  32. Line(T, b) → g_1
  33. Point(e_1) → G_1
  34. Prism(poly3, G_1) → u, C_1, face6, edge2, edge1, edge4, edge5, edge3, edge6, edge8, edge9, edge10, D_1, edge7, E_1, F_1, face1, face2, face5, face4, face3