Small Cylindrical Volumes Demo
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Multivariable Calculus
This example demonstrates how to calculate the volume of small cylindrical volumes using integration. Key math concepts include integration, volume calculation, inequalities, upper and lower sums or Riemann sums. GeoGebra commands used in construction are Segment, CircleArc, and objects like Δθ, ΔZ, Z, θ, r, Δr, T', Q', d, P, R, R', S, P', S', Q, T, a, b, c, f, h, g, e, i, j, k, l, p, q, s, t, dZ. Suitable for high school and above students learning the application of integration in volume calculations.
GeoGebra Commands & Parameters
Segment(Q', T') → dSegment(R, R') → aSegment(S, S') → bSegment(Q, T) → cSegment(P', Q) → fSegment(P, T') → hSegment(P', Q') → gSegment(P, T) → eSegment(R', Q) → iSegment(R, T) → jSegment(Q', S') → kSegment(T', S) → lCircleArc(P', Q, Q') → pCircleArc(P', R', S') → qCircleArc(P, R, S) → sCircleArc(P, T, T') → t