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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?

1. 7.75 cm
2. 8.25 cm
3. 6.32 cm
4. 9.45 cm

Correct answer: 6.32 cm

Solution

Since the cylinder is recast into 10 identical cones, their total volumes are equal. Equating \(\pi R^2 \cdot 8 = 10 \times \frac{1}{3}\pi \cdot 4^2 \cdot 6\) gives \(8R^2 = 320\), so \(R^2 = 40\) and \(R \approx 6.32\) cm.

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