B1. Jan prepared 30 liters of drink from fruit syrup and water in a ratio of 1:7. He poured the drink into a cylindrical container with an internal diameter of $32 \mathrm{~cm}$ and a height of $48 \mathrm{~cm}$.

A How much fruit syrup and how much water did he need for the drink?

B What is the volume of the container?

C How many centimeters was the surface of the poured drink below the top edge of the container?
B1. From the ratio 1:7, we write the equation $8 x=30$. The proportionality coefficient is $x=3.75$.

$x=3.75$ 1 point

Written answer: Jan needs $3.75 \ell$ of juice and $26.25 \ell$ of water. 1 point

B We use the formula for the volume of a cylinder

![](https://cdn.mathpix.com/cropped/2024_06_07_1ce1e4422095ce2d7960g-5.jpg?height=65&width=1613&top_left_y=627&top_left_x=307)

C The drink reaches a height

$v_{1}=\frac{V_{1}}{\pi r^{2}} \doteq \frac{30}{3.14 \cdot 1.6^{2}} \doteq 3.73 \mathrm{dm} \doteq 37 \mathrm{~cm}$.

The level of the poured drink is approximately

$v-v_{1}=48 \mathrm{~cm}-37 \mathrm{~cm}=11 \mathrm{~cm}$ below the rim of the pot.

1 point