A milk container is 8 cm long and 50 cm wide.

Length of the cuboidal milk container $=8 \mathrm{~cm}$

Breadth $=50 \mathrm{~cm}$

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

It is given that the container can hold $4 \mathrm{~L}$ of milk.

i. e., volume $=4 \mathrm{~L}=4 \times 1000 \mathrm{~cm}^{3}=4000 \mathrm{~cm}^{3}\left(\because 1 \mathrm{~L}=1000 \mathrm{~cm}^{3}\right)$

Now, volume of the container $=$ length $\times$ breadth $\times$ height

$\Rightarrow 4000=8 \times 50 \times h$

$\Rightarrow 4000=400 \times h$

$\Rightarrow h=\frac{4000}{400}=10 \mathrm{~cm}$

$\therefore$ The height of the milk container is $10 \mathrm{~cm}$.