Hello! Let me know if you find any errors in my solution.

The volume of a cylinder = \(\pi r^2h\)

We know:

\(v = 780 cm^3\)

\(h = 12cm\)

Now we plug in those values:

\(780 cm^3 = \pi r^2 12\)

And isolate the variable r:

\(\frac{780 cm^3}{12cm} = \pi r^2 \\\frac{65cm^2}{\pi} = r^2 \\r = \frac{\sqrt{65}cm}{\pi}\)

And round the radius to the nearest tenth:

\(r = \frac{\sqrt{65}}{\pi} \\r \approx \frac{8.1}{\pi} \\\pi \approx 3.1 \\r \approx \frac{8.1}{3.1} \approx \boxed{2.6 cm}\)

Therefore, the answer is \(\boxed{2.6 cm}\)

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