Freezer

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

Correct result:

V =  2.3768 l

Solution:

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

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