A vessel is in the form of a hemispherical bowl surmounted

Diameter of the hemisphere = 21 cm
Therefore, radius of the hemisphere = 10.5 cm

Volume of the hemisphere $=\frac{2}{3} \pi \mathrm{r}^{3}=\frac{2}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5=2425.5 \mathrm{~cm}^{3}$

Height of the cylinder $=$ Total height of the vessel-Radius of the hemisphere $=14.5-10.5=4 \mathrm{~cm}$

Volume of the cylinder $=\pi r^{2} h=\frac{22}{7} \times 10.5 \times 10.5 \times 4=1386 \mathrm{~cm}^{3}$

Total volume $=\mathrm{V}$ olume of hemispherical part $+\mathrm{V}$ olume of cylinder $=1386+2425.5=3811.5 \mathrm{~cm}^{3}$