7. Given that the volume of a cylinder is $V$ (a constant), then the minimum value of the total surface area of the cylinder is

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Note: The last sentence is a note in Chinese, which is not part of the translation. The translation itself is provided above.
7. $3 \sqrt[3]{2 \pi V^{2}}$ Let the radius of the base of the cylinder be $r$, the height be $h$, and the total surface area be $S$, then $S=2 \pi r^{2}+2 \pi r h=2 \pi r^{2}+\pi r h+\pi r h \geqslant$ $3 \sqrt[3]{2 \pi^{3} r^{4} h^{2}}=3 \sqrt[3]{2 \pi V^{2}}$. The equality holds when $h=2 r$.