Hemispherical Function

Author

Eric W. Weisstein
September 14, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/HemisphericalFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HemisphericalFunction.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Code

HemisphereFunction[x_,y_]:=If[x^2+y^2<=1,Sqrt[1-x^2-y^2],0]

Plot

V5

Plot3D[HemisphereFunction[x,y],{x,-2,2},{y,-2,2},
PlotPoints->50,PlotRange->All,AspectRatio->.7]

V7

Plot3D[HemisphereFunction[x,y],{x,-2,2},{y,-2,2}]

Plot3D[HemisphereFunction[x,y],{x,-2,2},{y,-2,2},RegionFunction->(#1^2+#2^2<1&),BoxRatios->Automatic]

Volume

HemisphereFunction[x,y]

Integrate[HemisphereFunction[x,y],{x,-∞,∞},{y,-∞,∞}]

Integrate[If[(x^2)+(y^2)≤(a^2),(Sqrt[(a^2)-(x^2)-(y^2)]),0],{x,-∞,∞},{y,-∞,∞},Assumptions->a>0]