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5

We define a region by f[x_, y_] := (x - 5)^2 + y^2 - 3^2; reg2=ImplicitRegion[f[x, y] <= 0, {x, y}] reg2// Region Then the implicit equation of revolution is f[Sqrt[x^2 + y^2], z] <= 0. f[x_, y_] := (x - 5)^2 + y^2 - 3^2; reg3=ImplicitRegion[f[Sqrt[x^2 + y^2], z] <= 0, {x, y, z}] reg3//Volume RegionPlot3D[DiscretizeRegion[reg3, MaxCellMeasure -&...


3

The volume may be calculated either by a formula: V== 2 Pi^2 r^2 R 2 Pi^2 3^2 5 == 90 Pi^2 == 888.264 or using integration of 2 Pi x, the circumference of the circle a x/y point describes during rotation, over the x/y circle: NIntegrate[2 Pi x, {x, 2, 8}, {y, -Sqrt[9 - (x - 5)^2], Sqrt[9 - (x - 5)^2]}] alternatively, we may use the "ImplicitRegion&...


3

RevolutionPlot3D needs a parametric representation of the curve. For your circle, try this code, modified from the 2nd example in the documentation for RevolutionPlot3D: RevolutionPlot3D[{5 + 3 Cos[t], 3 Sin[t]}, {t, 0, 2 Pi}]


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