I'm studying something through the video Volume of Surface of Revolution.
To be more exact, from the time 26:22 ...
I was able to define the analysis section:
f[x_] := x^2; g[x_] := 4 x;
Plot[{f[x], g[x]}, {x, 0, 4}, PlotTheme -> "Detailed",Filling -> {1 -> {2}}]
I made an attempt using the RevolutionPlot3D
function. Which is not exactly what I want, because it did not generate me a solid.
RevolutionPlot3D[{f[x], g[x]}, {x, 0, 4}, {θ, 0, 2 π},
PlotTheme -> "Detailed"]
I imagine the most appropriate function is RegionPlot3D
, but I could not define the limits:
RegionPlot3D[
x^2 + y^2 + z^2 >= x^2 && x^2 + y^2 + z^2 <= 4 x, {x, 0, 4}, {y, -16,
16}, {z, -16, 16}, PlotTheme -> "Detailed", PlotPoints -> 20,
PlotRange -> All]
Finally, as the video instructed me, I was able to get the volume of the solid in question:
volume = N[Integrate[(16*x^2 - 4*x)*Pi, {x, 0, 4}]]
971.799
My question
How should I describe the RegionPlot3D function to get the correct graphic? And is it possible to get the volume of this solid using this function?