## 29. Math Puzzle 10/67

What is the length of the spatial diagonal of a cube whose surface area in $\mathrm{cm}^{2}$ numerically equals its volume in $\mathrm{cm}^{3}$?
According to the given condition, the equation $6 a^{2}=a^{3}$ holds. This results in $a=6 \mathrm{~cm}$. According to Pythagoras, the diagonal of a square is $a \sqrt{2}$, and the space diagonal of a cube is $a \sqrt{3}$. For the given cube, it follows that $d=6 \sqrt{3} \approx 10.4 \mathrm{~cm}$.