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plotting - Filling the empty space in RevolutionPlot3D


I'm wanting to plot the solid of revolution from the area between two functions such as: $1\leq x \leq e$ and $1 \leq y \leq 2 + ln(x)$, doing something like this:


f[x_]:=2+Log[x]
g[x_]:=1
RevolutionPlot3D[{{f[x]}, {g[x]}}, {x, 1, E},

 RevolutionAxis -> x, AxesOrigin -> {0, 0, 0},
 Boxed -> False, Mesh -> {5, 0}, PlotRange -> {{0, 3}, All},
 PlotStyle -> Opacity[0.5]]

plot


Is there a way to fill this empty space between $f(x)$ and $g(x)$?



Answer



This one doesn't need V10:


RegionPlot3D[ 1 < Sqrt[z z + y y] < 2 + Log[x], {x, 1, E}, {y, -4, 4}, {z, -4, 4}, 
              Mesh -> None, AspectRatio -> 1, PlotRange -> {{0, 4}, {-4, 4}, {-4, 4}}]


Mathematica graphics


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