MathPlotAI Logo MathPlotAI

Sphere Surface Area & Volume

Sphere Surface Area & Volume
Loading the math board and drawing, please wait…
2016-02-28 08:00
Solid GeometryGeometric Construction
This example demonstrates the calculation and visualization of sphere surface area and volume formulas. Key math concepts include sphere geometry, surface area formula (4πr²), volume formula (4/3πr³), and the application of π. Construction highlights involve GeoGebra commands like Circle, Point, Arc, Rotate, Segment, Midpoint, and If to build the sphere model and dynamically show the calculation process. Suitable for high school mathematics teaching or self-learning to understand sphere geometric properties and formula derivation.

GeoGebra Commands & Parameters

  1. Circle(P, R) → e
  2. Point(e) → B
  3. Arc(c, 3.141592653589793, 0) → f
  4. Rotate(c, 90*°, P) → d
  5. Rotate(R, 90*°, P) → D
  6. Rotate(L, 90*°, P) → E
  7. Arc(Rotate[c, 90*°, P], 3.141592653589793, 0) → g
  8. Segment(P, B) → a
  9. Midpoint(P, B) → C
  10. If(VolumeFormula ≟ 1, A) → I
  11. If(VolumeSolution ≟ 1, F) → J
  12. If(SurfaceAreaFormula ≟ 1, G) → K
  13. If(SurfaceAreaSolution ≟ 1, H) → M