Capacitance of a solid conducting sphere surrounded by a hollow concentric conducting sphere can be determined by considering the electrostatics principles.

1. Introduction:
Consider a solid conducting sphere (inner sphere) of radius R and a hollow concentric conducting sphere (outer sphere) of radius r, where r > R. Both spheres are made of conductive material, which means they have free charges that can redistribute themselves to neutralize any external electric field.

2. Capacitance:
Capacitance is a measure of an object's ability to store electrical energy in the form of an electric charge. It is defined as the ratio of the charge stored on the object to the potential difference across it.

3. Concept of Capacitance:
The capacitance of a conducting sphere is determined by its geometry. For a conducting sphere, the capacitance depends only on its radius and the permittivity of free space (ε₀), and is given by the formula:

C = 4πε₀R

Where C is the capacitance and R is the radius of the conducting sphere.

4. Capacitance of the Assembly:
In the given assembly, the solid conducting sphere is surrounded by a hollow concentric conducting sphere. The presence of the outer sphere does not affect the capacitance of the inner sphere, as the charges on the inner sphere redistribute themselves to neutralize any external electric field.

Therefore, the capacitance of the assembly is equal to the capacitance of the solid conducting sphere (inner sphere), which is given by:

C = 4πε₀R

5. Proportionality:
As we can see from the above equation, the capacitance (C) is directly proportional to the radius (R) of the conducting sphere. This means that if we double the radius of the sphere, the capacitance will also double. Similarly, if we halve the radius, the capacitance will be halved.

Therefore, the capacitance of the assembly is directly proportional to the radius of the solid conducting sphere.

6. Conclusion:
In conclusion, the capacitance of a solid conducting sphere surrounded by a hollow concentric conducting sphere is directly proportional to the radius of the solid conducting sphere. This is because the presence of the outer sphere does not affect the redistribution of charges on the inner sphere, and the capacitance is solely determined by the geometry of the inner sphere.