Answer
(a) $V_{ab} = 12 \,\text{V}$
(b) $V_{ab} = 24 \,\text{V}$
(c) $V_{ab} = 3 \,\text{V}$
Work Step by Step
(a) The battery supplies the capacitor with a potential $V_{ab}$ = 12 V and as the plates of the capacitor don't lose any charges after disconnecting the battery, the plates will keep the same potential
$$\boxed{V_{ab} = 12 \,\text{V}}$$
(b) The potential between the two plates is directly proportional to the distance between the plates, therefore, the voltmeter will read the two times the original reading when the distance is doubled
$$V_{ab} = 2 \times 12 \,\text{V} = \boxed{24 \,\text{V}}$$
(c) The potential is inversely proportional to the area of the plates and the radius of the plates
$$V \propto \dfrac{1}{r^2}$$
So, when the radius is doubled, the potential will decrease four times and becomes
$$V_{ab} = \dfrac{1}{4} \times 12 \,\text{V} = \boxed{3 \,\text{V}} $$
