旋转体的盘-圆筒法体积计算

GeoGebra 命令及参数

1. Intersect(g, l_c, (1, 1)) → P_{gc}
2. Intersect(f, l_c, (1, 2)) → P_{fc}
3. Min(abs(rad_f), abs(rad_g)) → rad_i
4. Max(abs(rad_f), abs(rad_g)) → rad_o
5. If(rad_o ≠ rad_f, f_i, f_i) → rwash_{3out}
6. Textfield(a) → inputBox_a
7. Textfield(b) → inputBox_b
8. Intersect(f, l_b, (3, 6)) → P_{fb}
9. Intersect(g, l_b, (3, 1.7320508075688772)) → P_{gb}
10. Intersect(f, l_a, (1, 2)) → P_{fa}
11. Intersect(g, l_a, (1, 1)) → P_{ga}
12. IntegralBetween(f, g, Min[x(P_{fa}), x(P_{ga})], Max[x(P_{fb}), x(P_{gb})]) → R
13. Segment((0, y_{rotation}), (0, If[abs(rad_f) ≥ abs(rad_g), y(P_{fc}), y(P_{gc})])) → r_o
14. Segment((0, y_{rotation}), (0, If[abs(rad_f) < abs(rad_g), y(P_{fc}), y(P_{gc})])) → r_i
15. Circle(P, rad_i, y = 0) → cs3_i
16. Circle(P, rad_o, y = 0) → cs3_o
17. Plane((x_i, y_{rotation}, rad_o), x = x_i) → pln3d
18. Textfield(n) → InputBox1
19. If(rad_o ≟ rad_f, If[sgn(rad_f) ≥ 0, f_i(x) - y_{rotation}, y_{rotation} - f_i(x)], If[sgn(rad_g) ≥ 0, g_i(x) - y_{rotation}, y_{rotation} - g_i(x)]) → r_{outer}
20. If(rad_o ≠ rad_f, If[sgn(rad_f) ≥ 0, f_i(x) - y_{rotation}, y_{rotation} - f_i(x)], If[sgn(rad_g) ≥ 0, g_i(x) - y_{rotation}, y_{rotation} - g_i(x)]) → r_{inner}
21. IntegralBetween((π * r_{outer}(x)^(2)) - r_{inner}(x)^(2), x, a, b) → volume
22. Circle(P, rad_i, y = 0) → cs3_{i2}
23. SelectedIndex(lstTraceOpt) → lstTOIndex
24. Intersect(rwash_{3out}, l_c, (1, 2)) → P_{oc}
25. If(rad_o ≠ rad_f, f_i, g_i) → rwash_{3in}
26. Intersect(rwash_{3in}, l_c, (1, 1)) → P_{ic}
27. Segment(P_{oc}, P_{ic}) → r_{fg}
28. Sequence(Segment[Rotate[P_{fc}, i°, l_r], Rotate[P_{gc}, i°, l_r]], i, 0, 360, 1) → wash_3
29. Sequence(Rotate[P_{oc}, i°, l_r], i, 0, 360, 1) → wash_{3o}
30. Sequence(Rotate[P_{ic}, i°, l_r], i, 0, 360, 1) → wash_{3i}
31. Textfield(tf) → InputBox_f
32. Textfield(tg) → InputBox_g