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Volume of a Tetrahedron Outside a Cylinder

Volume of a Tetrahedron Outside a Cylinder
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2018-09-14 16:15
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the volume calculation of a tetrahedron outside a cylinder. Key mathematical concepts include solid geometry and trigonometry. Using GeoGebra commands such as Polygon and Intersect, the tetrahedron is constructed and its volume is calculated. Suitable for high school or university-level solid geometry studies.

GeoGebra Commands & Parameters

  1. Pyramid(D, C, B, A) → b, faceBCD, edgeAB, faceACD, faceABC, faceABD, edgeCD, edgeBC, edgeBD, edgeAD, edgeAC
  2. IntersectPath(xOyPlane, a) → c
  3. Point(yAxis) → E
  4. OrthogonalLine(E, xOyPlane) → f
  5. Line(E, xAxis) → g
  6. Point(g) → F
  7. Point(f) → G
  8. Plane(G, E, F) → d
  9. IntersectPath(d, b) → poly1, H, I, J, K, h, i, j, k
  10. Intersect(j, a) → L, M
  11. Intersect(f, j) → N
  12. IntersectPath(d, a) → p
  13. Intersect(h, p) → O, P
  14. Intersect(edgeAC, a) → Q,
  15. Intersect(yAxis, zAxis) → R
  16. Plane(Q, C, R) → l
  17. IntersectPath(l, b) → 多角形1, S, T, U, m, n, q
  18. Intersect(m, h) → V
  19. Polygon(M, K, V, P) → q1, m_1, k_1, v, p_1

AI Drawing Prompt Reference

Draw a tetrahedron and a cylinder. The tetrahedron is outside the cylinder. First, construct the tetrahedron by connecting four vertices. Then, intersect the tetrahedron with the cylinder to find the intersection line. Draw the cylinder to ensure it overlaps with the tetrahedron partially. Finally, show the volume and shape of the tetrahedron outside the cylinder.
The prompt above was compiled from the original drawing commands and is for reference only.