VolumeVaultedSolid::usage="Calculate the volume of the vaulted solid below of: f[x, y] = 16 - - and above the elliptical region: + ≤ 1. References: Internet: Ronny on line; Personal.";
2
x
2
y
2
x
16
2
y
9
Development for volume:
Method 1:
In[]:=
V=zxy
3
∫
-3
4
9-
2
y
3
∫
-
4
3
9-
2
y
16--
2
x
2
y
∫
0
Out[]=
117π
Method 2 (suggested by the Ph.D Frank Kampas):
In[]:=
s1=ImplicitRegion[z<=16--,{x,y,z}];s2=ImplicitRegion+<=1,{x,y,z};s3=ImplicitRegion[z>=0,{x,y,z}];Volume@RegionIntersection[s1,s2,s3]
2
x
2
y
2
x
16
2
y
9
Out[]=
117π
Development for graph:
In[]:=
Solvez==16--,+==1,{x,z}
2
x
2
y
2
x
16
2
y
9
Out[]=
x-,x,z
4
3
9-
,z2
y
7
2
y
9
4
9-
2
y
3
7
2
y
9
Using my notebook Maxymin:
In[]:=
Maxymin[16--,{-5,5},{-5,5}]
2
x
2
y
Maximum: {0,0,16}
Out[]=
Null
Animation:
In[]:=
Manipulatef[x_,y_]:=16--;ShowPlot3Df[x,y],{x,-4,4},{y,-3,t1},BoxRatiosAutomatic,RegionFunctionFunction{x,y},+<=1,FillingBottom,PerformanceGoal->"Quality",AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PlotRange{{-4,4},{-3,3},{0,16}},ViewPoint{1.3,-2.4,0.5},ImageSize500,Style["Volume of a vaulted solid:",Bold,Large],{{t1,-3+0.00002,"Value (t1)"},-3+0.00001,3,0.00001},ControlPlacementTop
2
x
2
y
2
x
16
2
y
9
Out[]=
