Tower model

Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded.

The result is a three-digit number, and the control sum of all its digits is 6. It's a math toy for you.

Result

x2 =  150 cm

Solution:

$x_{ 1 } = 300 \cdot \ 100 = 30000 \ \\ m_{ 1 } = 8000 \cdot \ 1000 = 8000000 \ \\ m_{ 2 } = 1 \ \\ m \approx x^3 \ \\ k = \sqrt[3]{ m_{ 1 }/m_{ 2 }} = \sqrt[3]{ 8000000/1} = 200 \ \\ x_{ 2 } = x_{ 1 }/ k = 30000/ 200 = 150 = 150 \ \text{ cm }$

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