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Volume of a Rotated Solid

Volume of a Rotated Solid
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2015-11-15 23:16
FunctionSolid GeometryCalculusIntegral
This example demonstrates how to generate a 3D solid of revolution from a 2D curve and calculate its volume. Key math concepts include volume formulas for solids of revolution, integral calculus, function graphing, and geometric transformations. Construction highlights involve commands like CurveCartesian for curve plotting, Rotate for rotation, Surface for surface creation, Sequence and Sum for sequence and summation, and Integral for integral computation. Suitable for high school and above students studying solid geometry, calculus, and related applications.

GeoGebra Commands & Parameters

  1. CurveCartesian(t^(2), t, 0, t, 0, 3) → b
  2. Rotate(b, c, xAxis) → b'
  3. Surface(u^(2) + v^(2), u, v, u, -3, 3, v, -3, 3) → a
  4. Sequence(Cylinder[((9 * (n - 1) / m), 0), ((9 * n / m), 0), sqrt((9 * n / m))], n, 1, m) → list1
  5. Sum(list1) → d
  6. Sequence(Cylinder[((9 * (n - 1) / m), 0), ((9 * n / m), 0), sqrt((9 * n / m))], n, 1, m) → list1_1
  7. Sum(list1_1) → d_1
  8. Integral(x, 0, 9) → e