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Cylinder and Cone Intersection Demo

Cylinder and Cone Intersection Demo
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2018-05-08 06:04
Coordinate GeometrySolid GeometryParametric EquationGeometric Construction
This example demonstrates the intersection of a cylinder and a cone, forming a complex three-dimensional shape. Key mathematical concepts include solid geometry, intersection, and the representation of 3D figures. Construction highlights involve using GeoGebra commands like CurveCartesian for curves and Surface for surfaces, along with objects such as rotasi (rotating body), rotano (rotation), ejessi (intersection), ejesno (axes), botón3 (button), botón1 (button), Opac (opacity), rastrono (grid), and variables like b, r, a, d, objects c1, c2, g, and geometric figures cil (cylinder) and con (cone). Suitable for high school and above students studying solid geometry and intersection concepts.

GeoGebra Commands & Parameters

  1. CurveCartesian((a * cos(t)), sqrt((r^(2) * (d + (a * sin(t)))^(2)) - (a^(2) * cos(t)^(2))), d + (a * sin(t)), t, 0, (2 * π)) → c1
  2. CurveCartesian((a * cos(t)), (-sqrt((r^(2) * (d + (a * sin(t)))^(2)) - (a^(2) * cos(t)^(2)))), d + (a * sin(t)), t, 0, (2 * π)) → c2
  3. Surface((a * cos(u)), v, d + (a * sin(u)), u, 0, (2 * π), v, -5, 5) → cil
  4. Surface(((r * u) * cos(v)), ((r * u) * sin(v)), u, u, -5, 5, v, 0, (2 * π)) → con