A cuboidal vessel is 10 cm long and 5 cm wide.

Let $h \mathrm{~cm}$ be the height of the cuboidal vessel.

Given :

Length $=10 \mathrm{~cm}$

Breadth $=5 \mathrm{~cm}$

Volume of the vessel $=300 \mathrm{~cm}^{3}$

Now, volume of a cuboid $=$ length $\times$ breadth $\times$ height

$\Rightarrow 300=10 \times 5 \times h$

$\Rightarrow 300=50 \times h$

$\therefore h=\frac{300}{50}=6 \mathrm{~cm}$