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Surface Area of a Sphere by Jennifer Silverman

Surface Area of a Sphere by Jennifer Silverman
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2017-05-30 21:02
CircleSolid GeometryGeometric Construction
This example demonstrates the dynamic calculation of a sphere's surface area. Key math concepts include sphere geometry, surface area formula, and analytical geometry. GeoGebra commands and objects used are Intersect, Circle, Segment, OrthogonalLine, Polygon, Sphere, Sequence, and Point. Suitable for high school students learning solid geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(circle, l_5, 1) → B
  2. Circle(B, (π / 2 * radius)) → c_1
  3. Intersect(c_1, l_5, 1) → L
  4. Segment(L, B) → o
  5. Intersect(xAxis, yAxis) → A
  6. Circle(A, o) → c_2
  7. Intersect(c_2, yAxis, 2) → D
  8. Segment(A, D) → p_2
  9. Circle(B, Radius[circle]) → c_3
  10. Intersect(circle, p_2, 1) → F
  11. Intersect(circle, yAxis, 1) → G
  12. OrthogonalLine(F, p_2) → l_3
  13. OrthogonalLine(G, yAxis) → l_1
  14. Intersect(l_4, l_3) → I
  15. Intersect(l_4, l_1) → J
  16. Intersect(l_2, l_1) → K
  17. Intersect(l_2, l_3) → H
  18. Polygon(J, K, H, I) → poly1, n, l, k, m
  19. Segment(A, F) → p
  20. Segment(A, B) → u_1
  21. Intersect(m, xAxis) → E
  22. Intersect(l, xAxis) → C
  23. Sphere(B_1, A_1) → o_1
  24. Sequence((radius * cos((π * w / ((2 * b))))), w, 0, b) → list3
  25. Sequence(((Element[list3, w] * π), (p_2 * (w - 1) / b)), w, 1, b) → list4
  26. Sequence((0, (p_2 * t / b)), t, 0, b, 1) → list1
  27. Sequence((0, (p * t / b)), t, 0, b, 1) → list2
  28. Sequence(Segment[Element[list1, u], Point[Circle[Element[list1, u], Element[list4, u]]]], u, 1, b) → list5
  29. Polygon(F, H, C, A) → poly3, f, h, e, d
  30. Point(list4) → N
  31. Point(list4) → O
  32. Point(list4) → P
  33. Point(list4) → Q
  34. Point(list4) → R
  35. Point(list4) → S
  36. Point(list4) → T
  37. Point(list4) → U
  38. Point(list4) → V
  39. Point(list4) → W
  40. Point(list4) → Z
  41. Point(list4) → C_1
  42. Point(list4) → D_1
  43. Point(list4) → E_1
  44. Point(list4) → F_1
  45. Point(list4) → G_1
  46. Point(list4) → H_1
  47. Point(list4) → I_1
  48. Point(list4) → J_1
  49. Point(list4) → K_1
  50. Point(list1) → L_1
  51. Point(list1) → M_1
  52. Polygon(N, O, Z, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, P, L_1, M_1, Q, R, S, T, U, V, W) → poly2, n_1, w, z_1, c_4, d_1, e_1, f_1, g_1, h_1, i_1, j_1, o_2, k_1, l_6, m_1, p_1, q, r, s, t, u, v

AI Drawing Prompt Reference

Draw a sphere and demonstrate the dynamic calculation of its surface area. Start by drawing a circle, find its intersection with a vertical line, and use this point to draw a larger circle. Locate the intersection of this larger circle with the vertical line and connect these two points. Draw a circle with this line segment as the diameter. Then, find the intersection of this circle with the vertical line and connect it to the center of the sphere. Finally, form a polygon using these points and lines, and use sequences to generate multiple points, connecting them to dynamically display the surface area of the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.