Volume of Revolution Example by John Stenger

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. Point(xAxis) → B
3. Intersect(f, b, (5, 3.23606797749979)) → D
4. Intersect(f, a, (1, 2)) → C
5. Segment(A, C) → d
6. Segment(B, D) → e
7. Sequence((x(A) + (k * Δx), (f(x(A) + (k * Δx)) * cos(ϕ)), (f(x(A) + (k * Δx)) * sin(ϕ))), k, 0, n - 1) → tracepoints
8. Textfield(f) → inputBox1
9. Textfield(axis) → inputBox2
10. Sequence(Surface[x(A) + (u * Δx), axis + ((f(x(A) + (k * Δx)) - axis) * cos(v)), ((f(x(A) + (k * Δx)) - axis) * sin(v)), u, k, k + 1, v, 0, ϕ], k, 0, n - 1) → surfaces
11. Surface(x(A) + (u * Δx), axis + ((f(x(A) + ((i - 1) * Δx)) - axis) * cos(v)), ((f(x(A) + ((i - 1) * Δx)) - axis) * sin(v)), u, i - 1, i, v, 0, ϕ) → surface_{i}
12. Sequence(Polygon[(x(A) + (k * Δx), axis), (x(A) + (k * Δx), f(x(A) + (k * Δx))), (x(A) + ((k + 1) * Δx), f(x(A) + (k * Δx))), (x(A) + ((k + 1) * Δx), axis)], k, 0, n - 1) → rectangles
13. Polygon((x(A) + ((i - 1) * Δx), axis, 0), (x(A) + ((i - 1) * Δx), axis + ((f(x(A) + ((i - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((i - 1) * Δx)) - axis) * sin(ϕ))), (x(A) + (i * Δx), axis + ((f(x(A) + ((i - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((i - 1) * Δx)) - axis) * sin(ϕ))), (x(A) + (i * Δx), axis, 0)) → face_{i}, c, j, k, l
14. Sequence(CircumcircleSector[(x(A) + (k * Δx), f(x(A) + ((i - 1) * Δx)), 0), (x(A) + (k * Δx), axis + ((f(x(A) + ((i - 1) * Δx)) - axis) * cos(ϕ / 2)), ((f(x(A) + ((i - 1) * Δx)) - axis) * sin(ϕ / 2))), (x(A) + (k * Δx), axis + ((f(x(A) + ((i - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((i - 1) * Δx)) - axis) * sin(ϕ)))], k, i - 1, i) → endcaps_{i}
15. Sequence(Polygon[(x(A) + ((k - 1) * Δx), axis, 0), (x(A) + ((k - 1) * Δx), axis + ((f(x(A) + ((k - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((k - 1) * Δx)) - axis) * sin(ϕ))), (x(A) + (k * Δx), axis + ((f(x(A) + ((k - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((k - 1) * Δx)) - axis) * sin(ϕ))), (x(A) + (k * Δx), axis, 0)], k, 1, n) → faces
16. Sequence(CircumcircleSector[(x(A) + (k * Δx), f(x(A) + (k * Δx)), 0), (x(A) + (k * Δx), axis + ((f(x(A) + (k * Δx)) - axis) * cos(ϕ / 2)), ((f(x(A) + (k * Δx)) - axis) * sin(ϕ / 2))), (x(A) + (k * Δx), axis + ((f(x(A) + (k * Δx)) - axis) * cos(ϕ)), ((f(x(A) + (k * Δx)) - axis) * sin(ϕ)))], k, 0, n - 1) → endcaps_{left}
17. Sequence(CircumcircleSector[(x(A) + (k * Δx), f(x(A) + ((k - 1) * Δx)), 0), (x(A) + (k * Δx), axis + ((f(x(A) + ((k - 1) * Δx)) - axis) * cos(ϕ / 2)), ((f(x(A) + ((k - 1) * Δx)) - axis) * sin(ϕ / 2))), (x(A) + (k * Δx), axis + ((f(x(A) + ((k - 1) * Δx)) - axis) * cos(ϕ)), ((f(x(A) + ((k - 1) * Δx)) - axis) * sin(ϕ)))], k, 1, n) → endcaps_{right}
18. Polygon((x(A) + ((i - 1) * Δx), axis), (x(A) + ((i - 1) * Δx), f(x(A) + ((i - 1) * Δx))), (x(A) + (i * Δx), f(x(A) + ((i - 1) * Δx))), (x(A) + (i * Δx), axis)) → rectangle_{i}, g, m, p, q
19. Sequence(Cylinder[(x(A) + (k * Δx), axis, 0), (x(A) + ((k + 1) * Δx), axis, 0), f(x(A) + (k * Δx)) - axis], k, 0, n - 1) → cylinders
20. Surface(t, axis + ((f(t) - axis) * cos(u)), ((f(t) - axis) * sin(u)), t, x(A), x(B), u, 0, ϕ) → surface_{whole}
21. CircumcircleSector((x(A), f(x(A)), 0), (x(A), axis + ((f(x(A)) - axis) * cos(ϕ / 2)), ((f(x(A)) - axis) * sin(ϕ / 2))), (x(A), axis + ((f(x(A)) - axis) * cos(ϕ)), ((f(x(A)) - axis) * sin(ϕ)))) → endcap_{A}
22. CircumcircleSector((x(B), f(x(B)), 0), (x(B), axis + ((f(x(B)) - axis) * cos(ϕ / 2)), ((f(x(B)) - axis) * sin(ϕ / 2))), (x(B), axis + ((f(x(B)) - axis) * cos(ϕ)), ((f(x(B)) - axis) * sin(ϕ)))) → endcap_{B}