A cylinder is melted and recast into 10 identical cones, each with radius 4 cm and height 6 cm. What was the radius of the original cylinder if its height was 8 cm?

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Accepted Answer

1. Volume of one cone: $V_{cone}=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\cdot4^2\cdot6=32\pi$.  
2. Ten cones total: $10	imes32\pi=320\pi$.  
3. Cylinder volume equals this: $\pi R^2\cdot8=320\pi$.  
4. So $R^2=40$, $R=\sqrt{40}=2\sqrt{10}\approx6.32$ cm.  
FINAL_ANSWER: c

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