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I want to know what ranges must be set for theta and to get a hemisphere of radius 5 from SphericalPlot3D.

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And if you want a hemisphere in an arbitrary orientation you can do this.

normal = {1, 3, 2};
SphericalPlot3D[5, {θ, 0, π}, {ϕ, 0, 2 π}, 
 RegionFunction -> Function[{x, y, z, θ, ϕ, r}, {x, y, z}.normal >= 0]]

enter image description here

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Nice solution. Makes it easy to get the cut anywhere you like. – Sjoerd C. de Vries Nov 8 '13 at 7:36
 SphericalPlot3D[5, {θ, 0, π}, {ϕ, 0, π}]

enter image description here

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Depends on the orientation you want. bill s' answer makes a meridianal cut, one common way to cut the sphere in half. Here is another. This one make an equatorial cut.

SphericalPlot3D[5, {θ, 0, π/2}, {ϕ, 0, 2 π}]

plot.pngenter image description here

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