Juice box 2

The box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm, and 32 cm. Suppose the box stays at the smallest base juice level and reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the base will reach the juice level if the box flips 90° around its shortest side?

Final Answer:

V =  8.4 l
x =  2.5 cm

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ b=20\text{cm} \\ c=32\text{cm} \\ d=4\text{cm} \\ {S}_1=a\cdot b=15\cdot 20=300{\text{cm}}^2 \\ {V}_1=S_1\cdot (c-d)=300\cdot (32-4)=8400{\text{cm}}^3 \\ V=V_1\to \text{l}=V_1:1000\text{l}=8400:1000\text{l}=8.4\text{l}=8.4\text{l} \end{gathered}$$

$$\begin{gathered} S_2=a\cdot c=15\cdot 32=480 \\ {V}_2=S_1\cdot d=300\cdot 4=1200{\text{cm}}^3 \\ x=\frac{V_2}{S_2}=\frac{1200}{480}=2.5\text{cm} \end{gathered}$$

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