How many solid lead balls each of diameter 2 mm can be made from a solid lead ball of radius 8 cm?

Explanation

Radius of the large ball R = 8 \text{ cm} = 80 \text{ mm}. Radius of the small ball r = \frac{2}{2} = 1 \text{ mm}. Since volume is conserved, the number of balls n = \frac{\text{Volume of large ball}}{\text{Volume of small ball}} = \frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3} = (\frac{80}{1})^3 = 512000.

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