Discussion
Spherical metal ball of radius 6 cm is melted and casted into small spherical balls having diameter 6 mm. How many small balls can be casted
Answer: A
The number of small balls is 8000.
Volume is conserved, and the number of balls is the ratio of the volumes, which is the cube of the ratio of radii. The large radius is 6 cm = 60 mm; the small radius is 3 mm:
\[ n = \left(\frac{60}{3}\right)^{3} = 20^{3} = 8000 \]
1000 comes from using the small diameter (6 mm) as if it were the radius, and the other options do not cube the ratio.
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