Volumes of Cylinders

GeoGebra Commands & Parameters

1. Sequence(Polygon[(a + (i * deltax), 0), (a + ((i + 1) * deltax), 0), (a + ((i + 1) * deltax), f(a + ((i + 1) * deltax))), (a + (i * deltax), f(a + ((i + 1) * deltax)))], i, 0, n - 1, 1) → list1, {5.656854249492381, 8, 9.797958971132712, 11.31370849898476, 12.649110640673516, 13.856406460551028, 14.966629547095764, 16}
2. Rotate(list1, α, y = 0) → list1'
3. Intersect(i, l) → B
4. Intersect(k, l) → C
5. Intersect(j, k) → D
6. Polygon(C, B, A, D) → poly1, c_2, b_1, a_1, d
7. Rotate(C, α, y = 0) → C'
8. Rotate(B, α, y = 0) → B'
9. Rotate(A, α, y = 0) → A'
10. Rotate(D, α, y = 0) → D'
11. Polygon(C', B', A', D') → poly1', c', b', a', d'
12. Sequence((a + (i * deltax), 0), i, 0, n, 1) → list2, {(0, 0), (2, 0), (4, 0), (6, 0), (8, 0), (10, 0), (12, 0), (14, 0), (16, 0)}
13. Sequence((a + (i * deltax), f(a + (i * deltax))), i, 1, n, 1) → list3, {(2, 2.8284271247461903), (4, 4), (6, 4.898979485566356), (8, 5.656854249492381), (10, 6.324555320336759), (12, 6.928203230275509), (14, 7.483314773547883), (16, 8)}
14. Rotate(list3, α, y = 0) → list3'
15. Sequence((a + (i * deltax), f(a + ((i + 1) * deltax))), i, 0, n - 1, 1) → list4, {(0, 2.8284271247461903), (2, 4), (4, 4.898979485566356), (6, 5.656854249492381), (8, 6.324555320336759), (10, 6.928203230275509), (12, 7.483314773547883), (14, 8)}
16. Sequence(x = a + (i * deltax), i, 1, n, 1) → list6, {x = 2, x = 4, x = 6, x = 8, x = 10, x = 12, x = 14, x = 16}
17. Sequence(Segment[Element[list3, i], Element[list4, i]], i, 0, n, 1) → list5, {NaN, 2, 2, 2, 2, 2, 2, 2, 2}
18. Sequence(CircleSector[Element[list2, i + 1], Element[list3', i], Element[list3, i], xOyPlane], i, 1, n, 1) → list7, {9.564404300928928, 19.128808601857852, 28.693212902786772, 38.25761720371571, 47.82202150464464, 57.386425805573545, 66.95083010650248, 76.51523440743141}
19. Sequence(Cylinder[Element[list2, i], Element[list2, i + 1], f(Element[list2, i + 1])], i, 1, n, 1) → list8, {50.265482457436704, 100.53096491487338, 150.79644737231004, 201.06192982974682, 251.3274122871835, 301.5928947446201, 351.85837720205683, 402.1238596594935}
20. Sequence(Circle[Element[list2, i], f(Element[list2, i]), x = 0], i, 2, n + 1, 1) → list10, {X = (2, 0, 0) + (0, -2.8284271247461903 cos(t), 2.8284271247461903 sin(t)), X = (4, 0, 0) + (0, -4 cos(t), 4 sin(t)), X = (6, 0, 0) + (0, -4.898979485566356 cos(t), 4.898979485566356 sin(t)), X = (8, 0, 0) + (0, -5.656854249492381 cos(t), 5.656854249492381 sin(t)), X = (10, 0, 0) + (0, -6.324555320336759 cos(t), 6.324555320336759 sin(t)), X = (12, 0, 0) + (0, -6.928203230275509 cos(t), 6.928203230275509 sin(t)), X = (14, 0, 0) + (0, -7.483314773547883 cos(t), 7.483314773547883 sin(t)), X = (16, 0, 0) + (0, -8 cos(t), 8 sin(t))}
21. Circle((a, 0), f(a + deltax), x = 0) → p
22. Surface(q, α, xAxis) → e
23. Cylinder((x(A), 0), (x(A) - deltax, 0), y(A)) → o, r, s, t
24. Dilate(E, If[0 < u ≤ 1, 1 - u, 0], D) → E'
25. Dilate(F, If[0 < u ≤ 1, 1 - u, 0], A) → F'
26. Segment(E, E') → f_1
27. Segment(F, F') → g_1
28. Dilate(D, If[1 < u ≤ 2, 2 - u, 0], A) → D'_1
29. Segment(D, D'_1) → h_1
30. Rotate(F, α, y = 0) → F'_1
31. Rotate(F', α, y = 0) → F''
32. Segment(F'_1, F'') → i_1
33. Rotate(E, α, y = 0) → E'_1
34. Rotate(E', α, y = 0) → E''
35. Segment(E'_1, E'') → j_1
36. Rotate(D, α, y = 0) → D'_2
37. Rotate(D'_1, α, y = 0) → G
38. Segment(D'_2, G) → k_1
39. Textfield(f) → InputBox1
40. Textfield(a) → InputBox2
41. Textfield(b) → InputBox3
42. Integral(f, a, b) → m_1