Question: An exemple where solve/parametric does not provide the correct result

At the beginning was this problem asked to 11th-12th Grade students:
 

Let C a vertical cylinder of radius R_C = 10, and S a steel sphere of radius R = 4.
We place S into C and fill it with water up to the moment the water reaches the top of S.
Let V the volume of the water we used.
We then remove S and replaces it by another steel sphere S' with radius R' <> 4. Could it be that the free surface of the water reaches exactly the top of S'?
If it is so what is then the value of R'?

Mathematically does the equation (𝝅R_C²) ⨯ (2R) - (4 𝝅R_S³/3) = (𝝅R_C²) ⨯ (2R') - (4/3 𝝅R^'3), where R_C = 10 and R = 4, have other strictly positive solutions than the trivial one R' = R?

The answer here is yes: R' = 552^1/2 -2 ≅ 9.7473.. .

When I read this problem, I immediately asked myself the following question "Does a second sphere S' always exists whatever the values R_C > 0 and R ∊ (0, R_C]?".

In the attached worksheet I used two different Maple tools to answer this question:

• firstly solve+assumptions plus plots:-inequal to visualize the (R_C, R) domain where S' exists,
• next solve/parametric to present another way to get the characterization of this same domain.

The problem is that solve+assumptions and plots:-inequal both give the same correct result but solve/parametric does not.
PlotsInequal_vs_SolveParametric.mw

For this specific problem solve/parametric fails finding the correct result.
Is that a bug or did I misuse it?

Thanks in advance