Volumes of Spheres, Cones, and Cylinders

Volumes of Spheres, Cones, and Cylinders
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2018-10-23 08:52
This GeoGebra example demonstrates the calculation and comparison of volumes for spheres, cones, and cylinders. Key mathematical concepts include volume formulas (V_sphere=4/3πr³, V_cone=1/3πr²h, V_cylinder=πr²h) and their derivations. Construction uses Sphere, Cone, Cylinder commands to create 3D models, Volume command to compute volumes, with variable r controlling radius changes and text labels for formulas. Suitable for middle to high school mathematics, helping students understand volume concepts, master formula applications, and compare volumes of different solid figures. Ideal for solid geometry visualization teaching.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, r), r) → a
  2. Cone((0, 0, 0), (0, 0, (2 * r)), r) → b, c, d
  3. Cylinder((0, 0, 0), (0, 0, (2 * r)), r) → e, f, g, h
  4. Volume(a) → i
  5. Volume(b) → j
  6. Volume(e) → k