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Cone Volume and Surface Area

Cone Volume and Surface Area
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2013-08-10 01:20
Solid GeometryCalculusGeometric ConstructionSlider Animation
In collections Mensuration Area, perimeter and volume of shapes
This example demonstrates the calculation of cone volume and surface area, helping students review formulas and see the net of a cone. Key math concepts include volume formulas, surface area formulas, pi, geometric transformations, etc. GeoGebra commands and objects like If, Conic, Segment, Midpoint, Point, Distance, Rotate, CircleSector, Polygon, Intersect, Arc, Circumference, Angle, CircumcircleArc, Textfield are used in construction. Suitable for high school students to reinforce solid geometry knowledge and understand formula derivation and practical applications.

GeoGebra Commands & Parameters

  1. If(net < -1, (-net - 1) * 3, 0) → net_θ
  2. If(net < -1, 3 * (-net - 1) + 0.2, 0.2) → net_b
  3. If(net < -1, -1, net) → net_e
  4. If(net_e > -0.0010, 0, -net_e) → net_h
  5. Conic(A, B, C, D, E) → c
  6. If(net > 0, 1, 0) → net_1
  7. Conic(A, B, C, D, E) → d
  8. Segment(V, A') → b
  9. Segment(V, F') → e
  10. Midpoint(A', F') → M_{A'F'}
  11. Point(c) → G
  12. Conic(A', B', C', F', E') → k
  13. Conic(A', B', C', F', E') → p
  14. Distance(O, V) → distanceOV
  15. Segment(O_c, O_u) → l
  16. Rotate(O_o, θ * 2, V) → H
  17. Rotate(O_o, -θ * 2, V) → H'
  18. CircleSector(V, H', H) → q
  19. Polygon(V, A', F') → poly1, f', v, a
  20. Distance(V, H') → distanceVH'
  21. Segment(V, H) → b'
  22. Segment(V, H') → e'
  23. Intersect(p, b') → K, K_2
  24. Intersect(p, e') → J, J_2
  25. Segment(V, J_2) → g
  26. Segment(V, K_2) → i
  27. Arc(p, A', K_2) → t
  28. Arc(p, J_2, F') → f
  29. If(θ + 0.6 * θ_d < 2 * π * r / l_s * 0.5, θ + 0.6 * θ_d, 2 * π * r / l_s * 0.5) → θ_c
  30. Rotate(O_o, θ_c, V) → H_1
  31. Rotate(O_o, -θ_c, V) → H'_1
  32. CircleSector(V, H'_1, H_1) → c_2
  33. Circumference(c_2) → j
  34. Circumference(c) → circumferencec
  35. Distance(V, H'_1) → distanceVH'1
  36. Angle(H'_1, V, H_1) → α
  37. Point(c_2) → I
  38. CircumcircleArc(H', O_o, H) → c_1
  39. CircleSector(V, H'_1, H_1) → s
  40. Segment(M_{A'F'}, F') → m
  41. Segment(M_{A'F'}, V) → n
  42. Angle(F', M_{A'F'}, V) → β
  43. Midpoint(b) → M_{VA'}
  44. Textfield(r) → inputBox1
  45. Textfield(h) → inputBox2

AI Drawing Prompt Reference

Draw a cone with its net, showing the calculation of volume and surface area. The base and side of the cone unfold into a sector and a triangle, with key points, lines, and angles labeled. Use a slider to adjust the cone's height and base radius, dynamically displaying calculations and formulas. Start by drawing the 3D cone and its net, add auxiliary lines and labels, then incorporate sliders and text boxes for formulas and calculations.
The prompt above was compiled from the original drawing commands and is for reference only.