Cylindrical 6636

A cylindrical container with a bottom diameter of 30 cm and a height of 20 cm is filled with water. We want to pour the water into another cylindrical container with a bottom diameter of 15 cm. What minimum height must the second container have for the water to fit?

Correct answer:

h₂ =  80 cm

Step-by-step explanation:

$$\begin{gathered} D_1=30\text{cm} \\ {h}_1=20\text{cm} \\ {D}_2=15\text{cm} \\ {V}_1=V_2 \\ {S}_1{h}_1=S_2{h}_2 \\ {h}_1{D}_1^2=h_2{D}_2^2 \\ {h}_2=h_1\cdot \frac{D_1^2}{D_2^2}=20\cdot \frac{30^2}{15^2}=80\text{cm} \end{gathered}$$

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