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Surface Area of a Sphere by Juan Carlos Ponce Campuzano

Surface Area of a Sphere by Juan Carlos Ponce Campuzano
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2018-12-04 19:27
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the calculation of a sphere's surface area. Key mathematical concepts include the geometric properties of a sphere and the surface area formula. Using GeoGebra commands such as CurveCartesian and Surface, the example dynamically shows the changes in the sphere's surface area. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian((-R), 0, t, t, (-R), R) → Line
  2. Surface(((R * sin(((-u) * π / 4))) * cos(v)), ((R * sin(((-u) * π / 4))) * sin(v)), ((-R) * cos(((-u) * π / 4))), u, 0, 4, v, 0, (2 * π)) → Sphh
  3. CurveCartesian((R * sin((-t))), 0, ((-R) * cos((-t))), t, 0, π) → Sph
  4. Surface(((-R) * cos(v)), ((-R) * sin(v)), sin((((u / 4 * (2 * R)) - R) / 2 * π)), u, 0, 4, v, 0, (2 * π)) → Cyl
  5. Surface((((t * (-R)) + ((1 - t) * (R * sin(((-u) * π / 4))))) * cos(v)), (((t * (-R)) + ((1 - t) * (R * sin(((-u) * π / 4))))) * sin(v)), ((t * sin((((u / 4 * (2 * R)) - R) / 2 * π))) + ((1 - t) * ((-R) * cos(((-u) * π / 4))))), u, 0, 4, v, 0, (2 * π)) → SPH1
  6. Surface(((t - 1) * (-R)) + ((2 - t) * (R * cos((-u)))), ((t - 1) * ((u * R) - (π * R))) + ((2 - t) * (R * sin((-u)))), sin((((v / 4 * (2 * R)) - R) / 2 * π)), u, 0, (2 * π), v, 0, 4) → SPH2
  7. CurveCartesian(((-R), (((t * 2) * π) * R) - (π * R), R), t, 0, 1) → Up
  8. CurveCartesian(((-R), (-π), ((t * 2) * R) - R), t, 0, 1) → Side