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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 $\boxed{2.6 cm}$