How to plot 3D spherical graph using x y data?

Question

I have a problem in which the temperature is given at different radius for spherical ball. The temperature does not vary in theta and phi direction. The 2D representation is shown below:

The radius ranges from [0-112.5]. The data is given as:

r={0, 5.625, 11.25, 16.875, 22.5, 28.125, 33.75, 39.375, 45, 50.625, 56.25, 61.875, 67.5,73.125 78.75, 84.375, 90, 95.625, 101.25, 106.875, 112.5}

T={91.67957977, 91.67957977, 91.67957977, 91.67960856, 91.67960527, 91.6795804, 91.6793762, 91.67778452, 91.66602638, 91.58867628, 91.21715009, 90.23638055, 88.7682609, 87.08880295, 85.33335735, 83.57849684, 81.89021437, 80.34527736, 79.01720822, 77.9780673, 77.29413776}

I am trying to plot the above 2D graph into 3D spherical plot with different colors for temperature without any axis, but showing the scale for temperature similar to the graph shown below:

Thank you.

Answer 1

You could proceed as follows:

-Interpolate the data (delete the last element of T as Syed noted)

-Define a piecewise function that returns 0 for radius > data range

-Use DensityPlot3D with a region function

Here is the code:

fr = Interpolation[Transpose[{r, Most@T}]];
f1[x_, y_, z_] = 
  Piecewise[{{fr[Sqrt[x^2 + y^2 + z^2]], 
     Sqrt[x^2 + y^2 + z^2] < 113}, {0, True}}];

m = 113;
DensityPlot3D[f1[x, y, z], {x, -m, m}, {y, -m, m}, {z, -m, m}, 
 Axes -> False, RegionFunction -> Function[{x, y, z}, x < 0 || y > 0],
  ColorFunction -> Function[{z}, Hue[7 z]], OpacityFunction -> None]