B2. A cylindrical container with a radius of $4 \mathrm{~cm}$ and a height of $9 \mathrm{~cm}$ is filled with water to $\frac{2}{9}$ of its height. Mark decided to pour all the water into a conical container with a radius of $5 \mathrm{~cm}$ and a height of $6 \mathrm{~cm}$ (see figure). During the pouring, $5 \%$ of the water was spilled. How many deciliters of water are in the conical container and how high does the water reach (i.e., what is $|M P|$)?

(8 points)

![](https://cdn.mathpix.com/cropped/2024_06_07_70800c8f4239f8164bacg-12.jpg?height=474&width=677&top_left_y=228&top_left_x=1226)
B2.
Calculation of the amount of water $\mathrm{v}$ in a cylindrical container $V=\frac{2}{9} \pi \cdot r^{2} \cdot v=100.53 \mathrm{~cm}^{3}$ ..... 1 point
Calculation of the amount of water $\mathrm{v}$ in a conical container $0.95 \cdot V=95.5 \mathrm{~cm}^{3}$ ..... 1 point
Answer ..... 1 point
Writing the relationship between the radius of the water surface $r_{1}$ and the height of the water $v_{1}$ in the conical container $r_{1}$ ..... $v_{1}=5$ :
6 or $v_{1}=\frac{5 r_{1}}{6}$
1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_70800c8f4239f8164bacg-24.jpg?height=71&width=1464&top_left_y=484&top_left_x=176) ..... $1+1$ point
Calculation of the height of the water $v_{1} \doteq 5.1 \mathrm{~cm}$ ..... 1 point
Answer ..... 1 point