xdata = Table[x, {x, -1, 1, 0.05}];
ydata = Table[Sqrt[1 - x^2], {x, -1, 1, 0.05}];
circData = {Transpose[{xdata, ydata}], Transpose[{xdata, -ydata}]};
ListPlot[circData, Joined -> True, AspectRatio -> Automatic]

p = Plot3D[{1 + Sqrt[1 - y^2 - x^2 ], -1 -
     Sqrt[1 - y^2 - x^2 ]}, {x, -2, 2}, {y, -2, 2},
   PlotStyle -> {Orange}, Lighting -> Automatic, Mesh -> Automatic,
   BoxRatios -> Automatic, Boxed -> False, Axes -> None];
q = RegionPlot3D[
   Sqrt[x^2 + y^2] < 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
   PlotStyle -> {Orange}, Lighting -> Automatic, Mesh -> Automatic,
   BoxRatios -> Automatic, Boxed -> False, Axes -> None];
Show[p, q]