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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