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Solid with Circular Base and Isosceles Right Triangle Cross Sections

Solid with Circular Base and Isosceles Right Triangle Cross Sections
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2015-07-02 12:38
CircleSolid GeometryCalculusIntegralGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve BC Calculus Volumes in Calculus Volumes in Calculus
This example demonstrates a solid with a circular base and isosceles right triangle cross sections with the hypotenuse in the base. Key mathematical concepts include volume calculation in solid geometry. Using GeoGebra commands such as Circle, Polygon, Locus, and Integral, the solid can be constructed. Suitable for high school mathematics education or learning volume calculation in solid geometry.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 3) → c
  2. Polygon(C, B, A) → poly1, a_1, c_1, b_1
  3. Locus(C, s) → loc1
  4. Integral(9 - x^(2), -3, 3) → VolInt
  5. If(togV ≟ 0, "Show volume integral", "Hide volume integral") → ShowVolInteg
  6. If(togD ≟ 1, "Hide description", "Show description") → ShowDescrip
  7. Surface(u, v / ((-f(u)) ≤ v ≤ f(u)), 0, v, -3, 3, u, -3, 3) → Base
  8. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
  9. Angle(A, C, B) → α
  10. Surface(u, (v * f(u)), f(u) - (v * f(u)), u, -3, 3, v, 0, 1) → SurfaceFront
  11. Surface(u, ((-v) * f(u)), f(u) - (v * f(u)), u, -3, 3, v, 0, 1) → SurfaceBack
  12. Sequence(Polygon[(-3 + (k * h), f(-3 + ((k + p) * h)), 0), (-3 + (k * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), f(-3 + ((k + p) * h)), 0)], k, 0, m - 1) → SlicesBase
  13. Sequence(Polygon[(-3 + (k * h), f(-3 + ((k + p) * h)), 0), (-3 + (k * h), (-f(-3 + ((k + p) * h))), 0), (-3 + (k * h), 0, f(-3 + ((k + p) * h)))], k, 0, m - 1) → SidesLeft
  14. Sequence(Polygon[(-3 + ((k + 1) * h), f(-3 + ((k + p) * h)), 0), (-3 + ((k + 1) * h), (-f(-3 + ((k + p) * h))), 0), (-3 + ((k + 1) * h), 0, f(-3 + ((k + p) * h)))], k, 0, m - 1) → SidesRight
  15. Sequence(Surface[-3 + ((k + u) * h), ((v - 1) * f(-3 + ((k + p) * h))), (v * f(-3 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesFront
  16. Sequence(Surface[-3 + ((k + u) * h), ((1 - v) * f(-3 + ((k + p) * h))), (v * f(-3 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesBack
  17. Sequence(Area[Element[SidesLeft, k]], k, 1, m) → Areas