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Wedge Volume Calculation

Wedge Volume Calculation
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2020-12-18 12:29
Solid GeometryCalculusIntegral
This example demonstrates the calculation of the volume of a wedge using integral calculus and trigonometric functions. It involves constructing a 3D surface and labeling key parameters. Suitable for high school and above students learning about solid geometry and calculus applications.

GeoGebra Commands & Parameters

  1. Surface(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)), (v * zmin(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)))) + ((1 - v) * zmax(xmin, (u * ymin(xmin)) + ((1 - u) * ymax(xmin)))), u, 0, 1, v, 0, 1) → left
  2. Surface(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)), (v * zmin(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)))) + ((1 - v) * zmax(xmax, (u * ymin(xmax)) + ((1 - u) * ymax(xmax)))), u, 0, 1, v, 0, 1) → right
  3. Textfield(xmin) → textfield1
  4. Textfield(xmax) → textfield2
  5. Textfield(ymin) → textfield3
  6. Textfield(ymax) → textfield4
  7. Textfield(zmin) → textfield5
  8. Textfield(zmax) → textfield6
  9. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)), (v / 3 * zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))) + ((1 - v / 3) * zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → front
  10. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax))), zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → up
  11. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)), (v / 3 * zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)))) + ((1 - v / 3) * zmax((u / 3 * xmin) + ((1 - u / 3) * xmax), ymax((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → back
  12. Surface((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax))), zmin((u / 3 * xmin) + ((1 - u / 3) * xmax), (v / 3 * ymax((u / 3 * xmin) + ((1 - u / 3) * xmax))) + ((1 - v / 3) * ymin((u / 3 * xmin) + ((1 - u / 3) * xmax)))), u, 0, 3, v, 0, 3) → down

AI Drawing Prompt Reference

Draw a wedge with four faces: left, right, front, and back. The left and right faces are defined by two points, (xmin, ymin, zmin) and (xmax, ymax, zmax). The front and back faces are defined by these two points and a midpoint, (xmin+xmax)/3, ymin, zmin and (xmin+xmax)/3, ymax, zmax. Make sure all faces are correctly connected to form a wedge.
The prompt above was compiled from the original drawing commands and is for reference only.