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Sphere in a Cylinder by AMW0ng

Sphere in a Cylinder by AMW0ng
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2020-04-23 05:22
Solid GeometryGeometric Construction
This example demonstrates the geometric relationship of a sphere inscribed within a cylinder. Key math concepts include solid geometry, volume calculation, and geometric construction. GeoGebra commands used are Sphere, Cylinder, Intersect, etc. Suitable for high school students to understand the derivation of the sphere's volume formula and spatial visualization skills development.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. Circle((0, 0, 0), 1, space) → c
  3. Intersect(xAxis, yAxis) → A
  4. Circle(A, B) → d
  5. Cylinder(d, 1) → b, e, f
  6. Cylinder(d, -1) → g, h_1, i
  7. CurveCartesian(cos(t), sin(t), h, t, 0, 6.29) → j
  8. Point(j) → C
  9. Point(j) → D
  10. Point(j) → E
  11. Circle(C, D, E) → k
  12. CurveCartesian(2 + cos(t), sin(t), 1, t, 0, 6.29) → l
  13. Point(l) → F
  14. Point(l) → G
  15. Point(l) → H
  16. Circle(H, F, G) → p
  17. Cone(p, -1) → m, q, n
  18. CurveCartesian(2 + (h * cos(t)), (h * sin(t)), h, t, 0, 6.29) → o
  19. Point(o) → I
  20. Point(o) → J
  21. Point(o) → K
  22. Circle(I, J, K) → r