Eiffel Tower

Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material if it weighs is 2.4 kg?

Correct result:

Model height:  2 m

Solution:

h1=300 m m1=80001000=8000000 kg m2=2.4 kg  V=abh=k1hk2hh=k1k2h3=Kh3  ρ=m1V1=m2V2 m1V1=m2V2 m1Kh13=m2Kh23 m1h13=m2h23 m1m2=h13h23 m1m2=(h1h2)3  m1m23=h1h2  h2=h1/m1m23  h2=300800010002.432 mh_1 = 300 \ m \ \\ m_1 = 8000 \cdot 1000 = 8000000 \ kg \ \\ m_2 = 2.4 \ kg \ \\ \ \\ V = abh = k_1 h k_2 h h = k_1 k_2 h^3 = K h^3 \ \\ \ \\ \rho = \dfrac{ m_1}{V_1} = \dfrac{ m_2}{V_2} \ \\ \dfrac{ m_1}{V_1} = \dfrac{ m_2}{V_2} \ \\ \dfrac{ m_1}{ K h_1^3 } = \dfrac{ m_2}{ K h_2^3 } \ \\ \dfrac{ m_1}{ h_1^3 } = \dfrac{ m_2}{ h_2^3 } \ \\ \dfrac{ m_1}{m_2} = \dfrac{ h_1^3 }{ h_2^3 } \ \\ \dfrac{ m_1}{m_2} = (\dfrac{ h_1 }{ h_2 })^3 \ \\ \ \\ \sqrt[3]{ \dfrac{ m_1}{m_2} } = \dfrac{ h_1 }{ h_2 } \ \\ \ \\ h_2 = h_1 / \sqrt[3]{ \dfrac{ m_1}{m_2} } \ \\ \ \\ h_2 = \dfrac{300}{\sqrt[3]{\dfrac{8000 \cdot 1000}{ 2.4}}} \doteq 2 \ \text{m}



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