Question : A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum numbers (in integers) of such spheres can be made?
Option 1: 125
Option 2: 166
Option 3: 30
Option 4: 100
Correct Answer: 166
Solution :
According to the question
Number of small spheres = $\frac{\text{Volume of solid sphere}}{\text{Volume of small sphere}}$
= $\frac{\frac{4}{3}\pi (11)^{3}}{\frac{4}{3}\pi (2)^{3}}$
= $\frac{1331}{8}$
= $166.375 \approx 166$
Hence, the correct answer is 166.
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