Plot a function based on the value of another function

Question

Could anyone guide me on how to plot the function VR with the values of ρ that I get from solving the following eq.

eq = (2 - 7 a) + (1 - ρ)^(-1 - b) ρ (2 - 2 ρ + b ρ) == 0;

I'm trying to first plot the above function and based on the value of ρ I want to plot VR function which is:

10 (10 a*ρ + ρ (-2 - 3 a - 2 (1 - ρ^(-b) ρ))

for plotting the eq I'm doing the following

0<=a<=1 ; 0 <= ρ <= 1; 0 <= b <= 3
 eq = (2 - 7 a) + (1 - ρ)^(-1 - b) ρ (2 - 2 ρ + b ρ) == 0;
soln = First@ Solve[eq, a];
Show[ParametricPlot3D[{a /. soln, b, ρ}, {b, 0, 3}, {ρ, 0, 1}, 
   PlotRange -> {{0, 1}, {0, 3}, {0, 1}}, 
   AxesLabel -> (Style[#, 16] & /@ {"a", "b", "ρ"})], 
 ParametricPlot3D[{a, b, 0}, {a, 0, 2/7}, {b, 0, 3}]]

However, i dont know how to plot VR based on the values of ρ

Thanks

Answer 1

Parentheses are unbalanced in the second expression. So, let us assume that it is meant to be

f = 10 a*ρ + ρ (-2 - 3 a - 2 (1 - ρ^(-b) ρ))

If not, it can be corrected and the procedure below (edited based on OP's comment below) followed:

ParametricPlot3D[{a /. soln, b, f /. soln}, {b, 0, 3}, {ρ, 0, 1},
    PlotRange -> {{0, 1}, {0, 3}, {0, 1}}, 
    AxesLabel -> (Style[#, 16] & /@ {"a", "b", "VR"})]

where soln is obtained from 83393.