Volume of a Rectangular Prism - Dynamic GeoGebra Demo

Volume of a Rectangular Prism - Dynamic GeoGebra Demo
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2017-04-11 11:26
① This GeoGebra example dynamically demonstrates the volume of a rectangular prism, showing how length, width, and height determine the total volume. ② Core mathematical concepts include the solid geometry formula V = a × b × c, along with algebraic variables, quadratic functions, and piecewise functions used in auxiliary constructions. ③ Construction highlights: The Sequence command generates multiple lists (list1 to list6) that organize geometric elements, while variables a, b, c control the prism's dimensions; sliders or input fields allow real-time adjustment, updating the 3D model and volume value instantly. ④ Suitable for middle school to high school students learning introductory solid geometry and volume formulas, as well as for teachers demonstrating parameter-driven geometric relationships in class.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(n, a - n / 2), (n, ((-n)) / 2)], n, 0, b) → list1
  2. Sequence(Segment[(n + b, ((-b)) / 2 + n / 2), (n + b, ((-b)) / 2 + n / 2 + a)], n, 0, c) → list2
  3. Sequence(Segment[(0, a - n), (b, ((-b)) / 2 - n + a)], n, 0, a) → list3
  4. Sequence(Segment[(b, ((-b)) / 2 + n), (b + c, ((-b)) / 2 + n + c / 2)], n, 0, a) → list4
  5. Sequence(Segment[(n, ((-n)) / 2 + a), (n + c, c / 2 - n / 2 + a)], n, 0, b) → list5
  6. Sequence(Segment[(n, a + n / 2), (n + b, a + n / 2 - b / 2)], n, 0, c) → list6

AI Drawing Prompt Reference

Create a dynamic illustration showing how the volume of a rectangular prism is determined by its length, width, and height. Use sequence commands to generate multiple lists of line segments representing different edges of the prism. Adjust the dimensions a, b, and c using sliders or input fields to instantly update the 3D model and volume calculation based on the formula V = a × b × c.
The prompt above was compiled from the original drawing commands and is for reference only.