404. A cylindrical glass is filled with mercury. Calculate the force of pressure of the mercury on the side surface of the glass, if its height is 0.1 m, and the radius of the base is 0.04 m. The density of mercury is $13600 \mathrm{kg} / \mathrm{m}^{3}$.
Solution. Let's calculate the area of the circular strip:

$$
\Delta S=2 \pi r d x=0.08 \pi d x
$$

The elementary force of pressure is

$$
\Delta P=9.81 \cdot 136,00 \cdot 0.08 \pi d x=10673 \pi d x
$$

Therefore,

$$
P=\int_{0}^{0.1} 10673 \pi x d x=\left.10673 \pi \frac{x^{2}}{2}\right|_{0} ^{0.1}=53.37 \pi \approx 167.6(\mathrm{N})
$$