Surface Area of Pyramids and Cones

GeoGebra Commands & Parameters

1. Point(CircleArc[(0, 1), (1, 1), (0, 0)]) → SA_{Q}
2. Point(CircleArc[(0, 1), (1, 1), (0, 0)]) → A
3. Point(CircleArc[(0, 1), (1, 1), (0, 0)]) → Q
4. If(y(SA_{Q}) > 0, CircleArc[(0, 1), (0, 0), SA_{Q}], 6.283185307179586) → SA_{s}
5. Circle(SA_{P}, 1, yAxis) → SA_{p}
6. If(y(A) > 0, Angle[(0, 0), (0, 1), A], 6.283185307179586) → α
7. Sequence((sin((i * θ)), 1 - cos((i * θ))), i, 0, (2 * n)) → list1
8. Segment(E, (x(E) + 1, y(E))) → a
9. Point(a) → F
10. Min((2 * (x(F) - x(E))), 1) → k
11. Max((2 * (x(F) - x(E))) - 1, 0) → k'
12. Sequence(If[k < 1, (x(O) + ((l * sin((i * φ))) * cos((i * φ)) / sin(φ)), y(O) + ((l * sin((i * φ))) * sin((i * φ)) / sin(φ))), (x(O) + (l * i), y(O))], i, 0, (2 * n)) → list2
13. Sequence(Sector[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]]], i, 1, n) → list3
14. Sequence(Sector[Rotate[Rotate[Translate[Circle[(x(O) + 0, y(O) + 1), Element[list1, i]], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)], Rotate[Rotate[Translate[Element[list1, i + 1], Vector[Element[list1, i], Element[list2, i]]], (((-((2 * i) - 1)) * k) * θ / 2), Element[list2, i]], (180° * k'), (x(O) + (n * l) - sin(θ / 2) / 2, y(O) + cos(θ / 2) / 2)]], i, n + 1, (2 * n)) → list4
15. If(y(A) > 0, CircleArc[(0, 1), (0, 0), A], 6.283185307179586) → s
16. CircleArc((0, 1 / (1 - m)), O, L) → b
17. Segment((0, 0), (s, 0)) → d
18. Midpoint(d) → B'
19. CircleArc((0, 1), A, (0, 0)) → c
20. Midpoint(a) → C
21. Point(Segment[(0, 1), (s, 1)]) → D
22. Segment(D, (x(D), y(D) - 1)) → e
23. Midpoint(e) → G
24. CircleSector((0, 1), (0, 0), A) → f
25. Circle((0, 1), 1) → g
26. Midpoint(A, D) → H
27. Intersect(xOyPlane, SA_{p}) → SA_{D}, J
28. Segment(SA_{O}, SA_{A}) → SA_{a}
29. Rotate(SA_{D1}, SA_{α}, SA_{a}) → SA_{D'}
30. Circle(SA_{O}, SA_{D1}, SA_{a}) → SA_{c1}
31. CircumcircleArc(SA_{D1}, SA_{D}, SA_{D'}) → SA_{q}
32. Surface((u * cos(SA_{v})), (u * sin(SA_{v})) + 1, SA_{f}(u), u, 0, abs(x(SA_{D})), SA_{v}, -1.5708, ((3 * pi)) / 2 - (2 * SA_{γ})) → SA_{o}
33. Segment(SA_{P}, SA_{D1}) → SA_{a1}
34. Segment(SA_{P}, SA_{D'}) → SA_{i}
35. Angle(SA_{D1}, SA_{O}, SA_{A}) → SA_{β}