A rectangular vessel 22 cm by 16 cm by 14 cm is full of water.

Volume of the rectangular vessel $=22 \times 16 \times 14=4928 \mathrm{~cm}^{3}$

Radius of the cylindrical vessel $=8 \mathrm{~cm}$

Volume $=\pi \mathrm{r}^{2} \mathrm{~h}$

As the water is poured from the rectangular vessel to the cylindrical vessel, we have:

Volume of the rectangular vessel = volume of the cylindrical vessel

$\therefore$ Height of the water in the cylindrical vessel $=\frac{\text { volume }}{\pi \mathrm{r}^{2}}=\frac{4928 \times 7}{22 \times 8 \times 8}=\frac{28 \times 7}{8}=\frac{49}{2}=24.5 \mathrm{~cm}$