Eiffel Tower

The Eiffel Tower in Paris is 300 metres high and made of steel. It weighs 8,000 tonnes. If a model of the tower made of the same material weighs 2.8 kg, how tall is it?

Final Answer:

h₂ =  2.1 m

Step-by-step explanation:

$$\begin{gathered} h_1=300\text{m} \\ {m}_1=8000\text{t}\to \text{kg}=8000\cdot 1000\text{kg}=8000000\text{kg} \\ {m}_2=2.8\text{kg} \\ V=abh=k_{1}h{k}_{2}hh=k_1{k}_2{h}^3=K{h}^3 \\ {\rho }_1={\rho }_2 \\ \rho =m_1/V_1=m_2/V_2=const \\ {m}_1\cdot V_2=m_2\cdot V_1 \\ {m}_1\cdot (K\cdot h_2^3)=m_2\cdot (K\cdot h_1^3) \\ {m}_1\cdot h_2^3=m_2\cdot h_1^3 \\ {h}_2=\sqrt[3]{\frac{m_2}{m_1}}\cdot h_1=\sqrt[3]{\frac{2.8}{8000000}}\cdot 300=2.1\text{m} \end{gathered}$$

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