New answers tagged scripting
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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