Let two circles center $O_1$, radius $10$ and center $O_2$, radius $6$ so that $AB$ is a diameter of the circle center $O_2$. I am trying to draw solid when rotate the filled region around line $O_1O_2$.
Based on this answer I tried
Clear["Global`*"]; r1 = 10; r2 = 6; cir1[t_] := {r1 Cos[t], r1 Sin[t]}; cir2 [s_] := {8 + r2 Cos[s], r2 Sin[s]}; ParametricPlot[{{r1 Cos[t], r1 Sin[t]}, {8 + r2 Cos[s], r2 Sin[s]}}, {t, 0, 2 Pi}, {s, 0, 2 Pi}, Mesh -> False] reg = ParametricPlot[{{r1 Cos[t], r1 Sin[t]}, {8 + r2 Cos[s], r2 Sin[s]}}, {t, -ArcCos[4/5], ArcCos[4/5]}, {s, -Pi/2, Pi/2}, Mesh -> False] Show[RevolutionPlot3D[ cir1[t] // Evaluate, {t, -ArcCos[4/5], ArcCos[4/5]}, RevolutionAxis -> {1, 0, 0}], RevolutionPlot3D[cir2[s] // Evaluate, {s, -Pi/2, Pi/2}, RevolutionAxis -> {1, 0, 0}], PlotRange -> All, Boxed -> False, Axes -> False] To find the points $A, B$, I solve the system of equations
Solve[{(x - 8)^2 + y^2 == 36, x^2 + y^2 == 100}, {x, y}, Reals] {{x -> 8, y -> -6}, {x -> 8, y -> 6}}
I have to find the angle $\arccos(4/5)$ by hand.
{s0, t0} = {s, t} /. First@Solve[{cir2[s] == cir1[t], 0 <= s <= π, 0 <= t <= π}, {s, t}]$\endgroup$