Number of moles, $n=\frac{mass\left(m\right)}{\text{ molar mass }\left(M\right)}$

Given, radius $=1.0 \mathrm{cm}$

$\therefore$ volume $=\frac{4\pi }{3} {\mathrm{cm}}^3$

Given, density $=1.0 \mathrm{g} {\mathrm{cm}}^{-3}$,

$\therefore$ Mass $=$ volume $\times$ density $=\frac{4\pi }{3} \mathrm{g}$

(Atomic weight of water $=18$ )

$\therefore n=\frac{4\pi }{3\times 18}=\frac{2\pi }{27}$