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Solid of Revolution about x-axis

Solid of Revolution about x-axis
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2019-11-16 02:15
Solid GeometryCalculusIntegralGeometric Construction
This example demonstrates the solid formed by rotating a plane region around the x-axis. It involves core calculus concepts like integral calculations, rotation geometry, and volume computation. Constructed using GeoGebra commands and objects such as Textfield, CircleSector, Surface, Circle, and CurveCartesian. Suitable for high school and above students learning solid geometry and calculus applications.

GeoGebra Commands & Parameters

  1. Textfield(a) → inputa
  2. Textfield(b) → b1
  3. Textfield(f1) → inputf
  4. CircleSector((a, 0, 0), (a, f(a), 0), (a, 0, f(a)), xOyPlane) → sectorA11
  5. CircleSector((a, 0, 0), (a, 0, f(a)), (a, (-f(a)), 0), xOyPlane) → sectorA12
  6. CircleSector((b, 0, 0), (b, f(b), 0), (b, (f(b) * cos(umax)), (f(b) * sin(umax))), xOyPlane) → sectorB1
  7. Surface(t, (f(t) * cos(u)), (f(t) * sin(u)), t, a, b, u, 0, umax) → surf1
  8. Circle((cs, 0, 0), f(cs), x = 0) → crossSect
  9. CurveCartesian(t, (f(t) * cos(umax)), (f(t) * sin(umax)), t, a, b) → fcurve
  10. Surface(t2, ((u2 * f(t2)) * cos(umax)), ((u2 * f(t2)) * sin(umax)), t2, a, b, u2, 0, 1) → surfcap
  11. CircleSector((b, 0, 0), (b, f(b), 0), (b, (cos((5 * π / 6)) * f(b)), (sin((5 * π / 6)) * f(b))), xOyPlane) → sectorB11
  12. CircleSector((b, 0, 0), (b, (cos((2 * π / 3)) * f(b)), (sin((2 * π / 3)) * f(b))), (b, (cos((4 * π / 3)) * f(b)), (sin((4 * π / 3)) * f(b))), xOyPlane) → sectorB12
  13. CircleSector((b, 0, 0), (b, (cos((7 * π / 6)) * f(b)), (sin((7 * π / 6)) * f(b))), (b, (cos(π / 12) * f(b)), (sin(π / 12) * f(b))), xOyPlane) → sectorB13
  14. CircleSector((b, 0, 0), (b, (cos((2 * π / 3)) * f(b)), (sin((2 * π / 3)) * f(b))), (b, (f(b) * cos(umax)), (f(b) * sin(umax))), xOyPlane) → sectorB2
  15. CircleSector((b, 0, 0), (b, (cos((7 * π / 6)) * f(b)), (sin((7 * π / 6)) * f(b))), (b, (f(b) * cos(umax)), (f(b) * sin(umax))), xOyPlane) → sectorB3
  16. Circle((b, 0, 0), f(b), yzplane) → capb
  17. CircleSector((a, 0, 0), (a, f(a), 0), (a, (f(a) * cos(umax)), (f(a) * sin(umax))), xOyPlane) → sectorA1
  18. CircleSector((a, 0, 0), (a, (cos((2 * π / 3)) * f(a)), (sin((2 * π / 3)) * f(a))), (a, (f(a) * cos(umax)), (f(a) * sin(umax))), xOyPlane) → sectorA2
  19. CircleSector((a, 0, 0), (a, (cos((7 * π / 6)) * f(a)), (sin((7 * π / 6)) * f(a))), (a, (f(a) * cos(umax)), (f(a) * sin(umax))), xOyPlane) → sectorA3
  20. Circle((a, 0, 0), f(a), yzplane) → capa