## 244. Math Puzzle $9 / 85$

The Berlin TV Tower at Alexanderplatz has a height of 365 m. Its total mass is approximately 26000 t.

How large would a scale and detail-accurate model of the "Tele-asparagus" be if it were made of the same building materials as the original and had a mass of $1 \mathrm{~kg}$?
The difficulty of the task lay in the fact that with a scale reduction in the height of the TV tower, the other two dimensions would also shorten in the same scale. The ratio equation is:

$$
\frac{x \mathrm{~m}}{365 \mathrm{~m}}=\sqrt[3]{\frac{1 \mathrm{~kg}}{26000000 \mathrm{~kg}}} \quad, \quad x=\frac{365}{296} \approx 1.23 \mathrm{~m}
$$

Thus, the $1 \mathrm{~kg}$ model would be $1.23 \mathrm{~m}$ high.