## 239. Math Puzzle $4 / 85$

A round steel rod is to withstand a tensile force of 150000 N. The permissible stress of the steel grade used is $12000 \mathrm{~N} / \mathrm{cm}^{2}$.

How large must the diameter of the rod be? $(\pi=3.14)$
The steel rod needs an area to absorb the tensile force of

$$
A=\frac{F_{Z}}{\text { Load capacity }}=\frac{150000 \mathrm{~N} \cdot \mathrm{cm}^{2}}{12000 \mathrm{~N}}=12.5 \mathrm{~cm}^{2}
$$

For the circular area, the formula is: $A=\frac{\pi}{4} d^{2} ; d=\sqrt{\frac{4 \cdot 12.5 \mathrm{~cm}^{2}}{3.14}}=3.99 \mathrm{~cm}$.

The steel rod must have a diameter of $3.99 \mathrm{~cm}$ (approximately $4 \mathrm{~cm}$).