3. A cylindrical container with a base radius of $4 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ is filled with water. Determine the angle at which the container must be tilted relative to the base plane so that a quarter of the water spills out.
Solution.

From the figure, we see

$$
\operatorname{tg} \alpha=\frac{\frac{1}{4} v}{r}=1
$$

The container needs to be tilted at an angle of $\alpha=45^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_30_d793ff9f9da41a4dd093g-17.jpg?height=803&width=1011&top_left_y=241&top_left_x=637)