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Net of a Cone with Constant Slant Height

Net of a Cone with Constant Slant Height
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2019-07-01 23:25
Trigonometry
This example demonstrates the net of a cone with a constant slant height. Key mathematical concepts include cones, trigonometry, and geometric construction. Using GeoGebra commands such as Point, Segment, Circle, and Tangent, the net of the cone can be constructed. Suitable for high school geometry and solid geometry courses.

GeoGebra Commands & Parameters

  1. Point(Circle[A, radius]) → B
  2. Segment(A, B) → r
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Tangent(C, c) → f,
  6. OrthogonalLine(C, f) → g
  7. Point(Circle[C, slant]) → D
  8. Segment(C, D) → h
  9. Intersect(c, h, 1) → E
  10. Circle(D, E) → d
  11. Circumference(c) → circumferencec
  12. PointIn(c) → Pointc
  13. Rotate(D, ((360 * r / h))°, C) → D'
  14. Rotate(E, ((360 * r / h))°, D) → E'
  15. Angle(E, D, E') → α
  16. CircleSector(D, E, E') → e
  17. Distance(E, E') → distanceEE'
  18. Length(e) → a
  19. PointIn(e) → Pointe

AI Drawing Prompt Reference

Draw the net of a cone with a constant slant height. Start by drawing a circle with center A, then take a point B on the circle to form the radius of the cone's base. Draw circle A, then take a point C on the circle and draw the tangent line f at C, and draw a line g perpendicular to f. Take a point D on circle A and draw line CD, which intersects circle A at point E. Draw a circle with center D and radius DE. Draw the circumference of circle A and take a point F on it. Rotate points D and E to get D' and E', calculate the angle α of ∠DEF, draw sector DEE', and finally calculate the length of DE'.
The prompt above was compiled from the original drawing commands and is for reference only.