Task B-3.2. The axial section of a right circular cylinder is a square. Determine the length of the radius of the base so that its surface area and volume have the same numerical value.
## Solution.

From the condition that the axial section of the cylinder is a square, it follows that $2 r=h$.

Then from $O=V$ we get

$$
\begin{aligned}
2 r^{2} \pi+2 r \pi \cdot h & =r^{2} \pi \cdot h \\
2 r^{2} \pi+2 r \pi \cdot 2 r & =r^{2} \pi \cdot 2 r \\
6 r^{2} \pi & =2 r^{3} \pi
\end{aligned}
$$

From the last equation, it follows that $r=3$.