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Sphere vs Hemisphere Volume Comparison by ssommer

Sphere vs Hemisphere Volume Comparison by ssommer
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2012-02-24 02:46
Solid GeometryGeometric Construction
In collections Area, Surface Area, Volume--Nets
This example demonstrates the relationship between the volume of a sphere and a hemisphere with the same radius, visually comparing their volumes. Key math concepts include volume formulas, geometric comparisons, and spatial visualization. GeoGebra commands and objects used in construction are Segment, Circle, Intersect, Point, and Ellipse. Suitable for high school students and math enthusiasts needing geometric intuition.

GeoGebra Commands & Parameters

  1. Segment(B, A) → h
  2. Circle(B, D) → e
  3. Circle(A, Radius[e]) → f
  4. Intersect(e, f, 1) → E
  5. Intersect(e, f, 2) → F
  6. Segment(E, F) → b
  7. Intersect(h, b) → G
  8. Circle(G, r) → g
  9. Point(g) → K
  10. Point(g) → Hemisphere
  11. Ellipse(K, Hemisphere, M) → k
  12. Point(g) → N
  13. Segment(G, N) → radius