Freezer

The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, and 30 cm. A layer of ice 23 mm thick was formed on the freezer's inner walls (and on the opening). How many liters of water will drain if we dispose of the freezer?

Correct answer:

V =  2.3768 l

Step-by-step explanation:

$$\begin{gathered} a=1.2\text{dm} \\ b=1.0\text{dm} \\ c=3.0\text{dm} \\ h=2\cdot 0.23=0.46\text{dm} \\ {V}_1=a\cdot b\cdot c=1.2\cdot 1\cdot 3=\frac{18}{5}=3.6{\text{dm}}^3 \\ {V}_2=(a-h)\cdot (b-h)\cdot (c-h)=(1.2-0.46)\cdot (1-0.46)\cdot (3-0.46)\doteq 1.015{\text{dm}}^3 \\ {V}_3=V_1-V_2=3.6-1.015\doteq 2.585{\text{dm}}^3 \\ {V}_4=V_3\to {\text{cm}}^3=V_3\cdot 1000{\text{cm}}^3=2.585\cdot 1000{\text{cm}}^3=2585.016{\text{cm}}^3 \\ {\rho }_1=0.9167{\text{g/cm}}^3 \\ {m}_1={\rho }_1\cdot V_4=0.9167\cdot 2585.016\doteq 2369.6842\text{g} \\ {m}_2=m_1\to \text{kg}=m_1:1000\text{kg}=2369.6842:1000\text{kg}=2.36968\text{kg} \\ {\rho }_2=0.997{\text{kg/dm}}^3 \\ {V}_5=m_2/{\rho }_2=2.3697/0.997\doteq 2.3768{\text{dm}}^3 \\ V=V_5\to \text{l}=V_5\cdot 1\text{l}=2.3768\cdot 1\text{l}=2.377\text{l}=2.3768\text{l} \end{gathered}$$

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