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Cone and Cylinder Solids of Revolution

Cone and Cylinder Solids of Revolution
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2019-02-09 01:28
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates solids of revolution of cones and cylinders. Key mathematical concepts include solid geometry. Using GeoGebra commands such as Vector, Polygon, Sequence, etc., the rotation bodies of cones and cylinders can be constructed. Suitable for high school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Vector(1.1 * d * W_x) → u
  2. Vector(1.1 * d * W_y) → v
  3. Vector(1.1 * d * W_z) → w
  4. Polygon(1.1 * d * (W_x + W_y), 1.1 * d * (-W_x + W_y), 1.1 * d * (-W_x - W_y), 1.1 * d * (W_x - W_y)) → poly1, g, i, j, l
  5. Sequence(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y, i, 0, p) → list1
  6. Sequence(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y + k * W_z, i, 0, p) → list3
  7. CurveCartesian(x(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y), y(r * cos(0.125 * i) * W_x + r * sin(0.125 * i) * W_y), i, 0, p) → e_1
  8. CurveCartesian(x(r * cos(0.125 * t) * W_x + r * sin(0.125 * t) * W_y + k * W_z), y(r * cos(0.125 * t) * W_x + r * sin(0.125 * t) * W_y + k * W_z), t, 0, p) → e_2
  9. Sequence(Segment[A, Element[list1, i]], i, 1, p + 1) → list2
  10. Sequence(Segment[Element[list1, i], Element[list3, i]], i, 1, p + 1) → list4
  11. Sequence(Segment[(0, 0) + k * W_z, Element[list3, i]], i, 1, p + 1) → list5

AI Drawing Prompt Reference

Draw a cone and a cylinder as solids of revolution. First, create three vectors u, v, and w. Then, use these vectors to create a quadrilateral. Next, generate a series of points to form the outline of the cone and rotate it around the axis to create the cone's solid of revolution. Finally, generate a series of points to form the outline of the cylinder and rotate it around the axis to create the cylinder's solid of revolution.
The prompt above was compiled from the original drawing commands and is for reference only.