Vase water capacity

The cube-shaped vase contains 320 ml of water and reaches a height of 5 CM. How many milliliters of water can we pour into the vase so the water does not run out?

Final Answer:

x =  30 mm

Step-by-step explanation:

$$\begin{gathered} V_1=320\text{ml}\to {\text{cm}}^3=320\cdot 1{\text{cm}}^3=320{\text{cm}}^3 \\ h=5\text{cm} \\ {V}_1=h\cdot S_1 \\ {S}_1=V_1/h=320/5=64{\text{cm}}^2 \\ {S}_1=a^2 \\ a=\sqrt{S_1}=\sqrt{64}=8\text{cm} \\ {V}_2=a^3=8^3=512{\text{cm}}^3 \\ {h}_2=a-h=8-5=3\text{cm} \\ x=h_2\to \text{mm}=h_2\cdot 10\text{mm}=3\cdot 10\text{mm}=30\text{mm}=30\text{mm} \end{gathered}$$

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