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Sphere in a Cylinder by Natasha Mitrov

Sphere in a Cylinder by Natasha Mitrov
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2020-04-22 00:21
Coordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the geometric relationship of a sphere inscribed in a cylinder, focusing on volume calculation, solid geometry, and coordinate geometry. It uses commands like Sphere, Cylinder, and Intersect in GeoGebra. Suitable for high school students exploring sphere volume formulas and geometric properties.

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