RegionPlot3D[
z >= 0 &&
x^2 + y^2 + z^2 <= 16 &&
z <= Sqrt[x^2 + y^2],
{x, -4,4}, {y, -4, 4}, {z, 0, 4},
AxesLabel -> {x, y, z},
Mesh -> True,
PlotRange -> Full,
PlotPoints -> 500,
MaxRecursion -> 15,
WorkingPrecision -> 255]