Examples, Section 15.8
MAT329, Fall, 2015
Andy Long

#20,  p. 1049 (from previous section)

plotparaboloidtop=Plot3D[8-x^2-y^2,{x,-2,2},{y,-2,2}];
plotparaboloidbottom=Plot3D[x^2+y^2,{x,-2,2},{y,-2,2}];
Show[plotparaboloidtop,plotparaboloidbottom,PlotRange->All,ImageSize->{250}]

Integrate[r,{t,0,2Pi},{r,0,2},{z,r^2,8-r^2} ]

#26,  p. 1055

sphere=SphericalPlot3D[1,{phi,0,Pi},{theta,0,2Pi}];
cylinder=ParametricPlot3D[{Cos[theta]^2,Cos[theta]Sin[theta],z},{theta,-Pi/2,Pi/2},{z,-1,1}];
Show[sphere,cylinder ]

From http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf
p. 14
Thanks, Neil!

plotplane=Plot3D[8-x-y,{x,-2,2},{y,-2,2}]
plotparaboloid=Plot3D[4-x^2-y^2,{x,-2,2},{y,-2,2}];
plotcylinder=ParametricPlot3D[{2 Cos[t],2 Sin[t],z},{t,0,2 Pi},{z,0,12}];
Show[plotplane,plotparaboloid,plotcylinder,PlotRange->All,ImageSize->{250}]

Clear[z,r]
Integrate[z r,{t,0,2Pi},{r,0,2},{z,4-r Cos[t]-r Sin[t],8+r Cos[t]+r Sin[t]}]

#31,  p. 1056: Mt. Fuji!

radius=62000
height=12400
work=Integrate[z 200 r ,{th,0,2Pi},{z,0,height},{r,0,radius(1-z/height)} ]
N[%]