capacitor

Capacitance $C$ is given by: $C=\frac{Q}{V}$ , where $Q$ and $V$ are the amount of charge and voltage involved.

The voltage $V$ of a conducting sphere is given by: $V=\frac{Q}{4\pi\epsilon_0R}$ , where $\epsilon_0$ is the permittivity of space and $R$ is the radius of the sphere.

Therefore, the capacitance $C$ of a sphere is: $C=\frac{Q}{V}=4\pi\epsilon_0$ .

We note that volume of a sphere $V_s$ is proportional to radius $r^3$ or $V_s \propto r^3$ .

Therefore, $\frac{V_{s1}}{V_{s0}}=\frac{r^3}{r_1^3}=\frac{27}{1} \Rightarrow r_1^3=27r^3 \Rightarrow r_1=3r$ .

The new capacitance $C_1 = 4\pi \epsilon_0r_1= 4\pi \epsilon_0(3r)=3C_0$ . Therefore, capacitance becomes $\boxed{3}$ times of before.