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Net of a Cylinder by Cuemath

Net of a Cylinder by Cuemath
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2019-01-16 19:46
Solid Geometry
This example demonstrates the net of a cylinder, illustrating its geometric properties and the process of unfolding. It uses GeoGebra commands such as Point, Circle, Intersect, Line, and Rotate to show the side unfolding of a cylinder. Suitable for students at the junior high school level and above studying solid geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Cylinder(c, 3) → b, e, f
  5. Intersect(zAxis, e) → C,
  6. Line(C, xAxis) → a
  7. OrthogonalLine(D, xOyPlane) → g
  8. Circle(g, C) → k
  9. Rotate(Rotate[e, ϕ, a], ϕ, xAxis) → e'
  10. Rotate(Rotate[e, ϕ, a], ϕ, xAxis) → d
  11. Circle(A, B) → h
  12. If(t < 1, ((r * sin((-θ))), ((r * (1 - cos((-θ)))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos((-θ)))) * sin(ϕ))), ((-π), (-3 * sin(ϕ)), (3 * cos(ϕ)))) → E
  13. If(t < 1, ((r * sin(θ)), ((r * (1 - cos(θ))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos(θ))) * sin(ϕ))), (π, (-3 * sin(ϕ)), (3 * cos(ϕ)))) → F
  14. If(t < 1, ((r * sin((-θ))), ((r * (1 - cos((-θ)))) * cos(ϕ)), ((r * (1 - cos((-θ)))) * sin(ϕ))), (-3.141592653589793, 0, 0)) → G
  15. If(t < 1, ((r * sin(θ)), ((r * (1 - cos(θ))) * cos(ϕ)), ((r * (1 - cos(θ))) * sin(ϕ))), (3.141592653589793, 0, 0)) → H
  16. Segment(E, G) → m
  17. Segment(F, H) → n
  18. Line((0, 1, 0), zAxis) → p
  19. Circle(p, B) → q
  20. Circle(p, B) → s
  21. If(t < 1, Surface[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)) - (v * sin(ϕ)), (v * cos(ϕ)) + ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1, v, 0, 3], Surface[(π * u), ((-v) * sin(ϕ)), (v * cos(ϕ)), u, -1, 1, v, 0, 3]) → i
  22. If(t < 1, CurveCartesian[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)), ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1], CurveCartesian[(π * u), 0, 0, u, -1, 1]) → l
  23. If(t < 1, CurveCartesian[(r * sin((u * θ))), ((r * (1 - cos((u * θ)))) * cos(ϕ)) - (3 * sin(ϕ)), (3 * cos(ϕ)) + ((r * (1 - cos((u * θ)))) * sin(ϕ)), u, -1, 1], CurveCartesian[(π * u), (-3 * sin(ϕ)), (3 * cos(ϕ)), u, -1, 1]) → j

AI Drawing Prompt Reference

Draw the net of a cylinder, starting by creating two points A and B, then drawing a circle c with A and B as centers. Next, create a cylinder b, e, f with c as the base and a height of 3. Draw the intersection point C of the cylinder's height line with the base, then draw a horizontal line a through C. Draw a vertical line g perpendicular to the x-axis and create a circle k with g as the center. Rotate e around the a axis to get e' and d. Draw the radii h and k of the circle c, and finally draw the edge segments m and n of the net.
The prompt above was compiled from the original drawing commands and is for reference only.