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Cone Section and Wet Surface Ratio

Cone Section and Wet Surface Ratio
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2018-04-15 23:49
Solid GeometryProbability & Statistics
This example demonstrates the cross-section of a cone cut by a plane and calculates the ratio of the wet surface to the total surface area. Key mathematical concepts include cone, plane, cross-section, ratio, and area calculation. Using GeoGebra commands such as Cone and Intersect, students can visually understand geometric construction and ratio calculation. Suitable for high school geometry and probability & statistics courses.

GeoGebra Commands & Parameters

  1. Cone(B, A, R) → a, c, b
  2. Cone(C, A, r) → d, e, f
  3. Point(c) → F
  4. Segment(B, A) → i
  5. Segment(B, F) → j
  6. Segment(F, A) → k
  7. Line(C, j) → m
  8. Intersect(m, k) → G
  9. Segment(C, G) → n

AI Drawing Prompt Reference

Draw a cone with base center at point A and apex at point B, with base radius R. Then draw another cone with base center at point C and apex at point A, with base radius r. Next, take a point F on the base of the first cone, connect point B to A, then connect point B to F, and finally connect point F to A. Draw a line through point C and point B, which intersects the line connecting point F and A at point G. Finally, draw a line connecting point C and point G.
The prompt above was compiled from the original drawing commands and is for reference only.