An experiment

The three friends agreed to the experiment. At the same time, they all took out an empty cylindrical container on the windowsill and placed it so that it was horizontal. Everyone lives in a different village, and each used a container with a different bottom diameter. When they met the next day after the rain, they shared the results of their experiment. Jan's vessel had a bottom content of 400 mm² and measured a volume of 16 cm³, Charles's vessel had an area of 10 cm² and measured 0.4 dm³, and Wenceslas's vessel had a bottom area of 0.2 dm² and measured 0.4 l of water.

At what height from the bottom was the water level after the rain a) Jan, b) Charles, c) Wenceslas?

Correct answer:

a =  40 mm
b =  400 mm
c =  200 mm

Step-by-step explanation:

$$\begin{gathered} S_1=400{\text{mm}}^2 \\ {V}_1=16{\text{cm}}^3\to {\text{mm}}^3=16\cdot 1000{\text{mm}}^3=16000{\text{mm}}^3 \\ {V}_1=S_1\cdot a \\ a=V_1\mathrm{/}{S}_1=16000\mathrm{/}400=40\text{ mm} \end{gathered}$$

$$\begin{gathered} S_2=10{\text{cm}}^2\to {\text{mm}}^2=10\cdot 100{\text{mm}}^2=1000{\text{mm}}^2 \\ {V}_2=0.4{\text{dm}}^3\to {\text{mm}}^3=0.4\cdot 1000000{\text{mm}}^3=400000{\text{mm}}^3 \\ {V}_2=S_2\cdot b \\ b=V_2\mathrm{/}{S}_2=400000\mathrm{/}1000=400\text{ mm} \end{gathered}$$

$$\begin{gathered} S_3=0.2{\text{dm}}^2\to {\text{mm}}^2=0.2\cdot 10000{\text{mm}}^2=2000{\text{mm}}^2 \\ {V}_3=0.4\text{ l}\to {\text{mm}}^3=0.4\cdot 1000000{\text{mm}}^3=400000{\text{mm}}^3 \\ {V}_3=S_3\cdot c \\ c=V_3\mathrm{/}{S}_3=400000\mathrm{/}2000=200\text{ mm} \end{gathered}$$

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