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Three Dimensional Objects with the Same Volume

Three Dimensional Objects with the Same Volume
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2017-11-26 02:52
Solid GeometryGeometric Construction
This example demonstrates different 3D objects with the same volume. It involves the concept of volume and how to construct these objects using GeoGebra commands such as Point, Polygon, Circle, Prism, and Cylinder. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, C, B) → t1, b, a, c
  4. Circle(D, radius) → d
  5. Prism(t1, altitude) → e, E, edgeBG, edgeEF, edgeFG, edgeEG, F, G, faceACFE, faceBCFG, faceABGE, faceEFG, edgeAE, edgeCF
  6. Cylinder(d, altitude) → f, g, h

AI Drawing Prompt Reference

Draw three different 3D shapes with the same volume. First, create two points on the x-axis and connect them with a triangle. Then, build a prism with this triangle as the base and a custom height. Finally, construct a cylinder with the circumscribed circle of the triangle as the base and a custom height.
The prompt above was compiled from the original drawing commands and is for reference only.