Ice rink

A rectangular rink measuring 15m and 20m long needs to be covered with a layer of ice 4.5cm high. How many liters of water are needed to create ice?

Correct answer:

V =  12420 l

Step-by-step explanation:

$$\begin{gathered} a=15\text{m} \\ b=20\text{m} \\ c=4.5\text{cm}\to \text{m}=4.5:100\text{m}=0.045\text{m} \\ {V}_1=a\cdot b\cdot c=15\cdot 20\cdot 0.045=\frac{27}{2}=13.5{\text{m}}^3 \\ {\rho }_1=1000{\text{kg/m}}^3 \\ {\rho }_2=920{\text{kg/m}}^3 \\ m={\rho }_2\cdot V_1=920\cdot 13.5=12420\text{kg} \\ {V}_2=\frac{m}{{\rho }_1}=\frac{12420}{1000}=\frac{621}{50}=12.42{\text{m}}^3 \\ V=V_2\to \text{l}=V_2\cdot 1000\text{l}=12.42\cdot 1000\text{l}=12420\text{l}=12420\text{l} \end{gathered}$$

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