Final answer:
The capacitance of the cylindrical capacitor is 0.025 nF. The ratio of the radii of the cylinders is 1:1.
Step-by-step explanation:
The capacitance of a cylindrical capacitor can be calculated using the equation C = Q/V, where C is the capacitance, Q is the charge, and V is the potential difference. In this case, the charge is 0.500 nC and the potential difference is 20.0 V, so the capacitance is C = 0.500 nC / 20.0 V = 0.025 nF.
To find the ratio of the radii of the cylinders, we can use the equation for the volume of a cylinder V = πr^2h, where V is the volume, r is the radius, and h is the height. Since the volume of the cylinders is the same, we can write πr₁^2h = πr₂^2h, where r₁ and r₂ are the radii of the cylinders. Dividing both sides by πh, we get r₁^2 = r₂^2, or r₁ = r₂. Therefore, the ratio of their radii is 1:1.