Question : The number of lead balls, each 3 cm in diameter, that can be made from a solid lead sphere of diameter 42 cm is:
Option 1: 2744
Option 2: 4722
Option 3: 7244
Option 4: 2742
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Correct Answer: 2744
Solution :
Given: A solid lead sphere of diametre 42 cm.
The radius of a solid sphere is 21 cm.
The radius of a small sphere = $\frac{3}{2}$ = 1.5 cm.
The volume of the sphere of radius $r$ is $\frac{4}{3}\pi r^3$.
Let $x$ be the total number of lead balls that can be made.
According to the question,
⇒ $\frac{4}{3}\times\pi \times(21)^3=x\times\frac{4}{3}\times\pi \times(1.5)^3$
⇒ $x=\frac{21\times 21\times 21\times 1000}{15\times 15\times 15}=7\times 7\times 7\times 2\times 2\times 2=2744$
Hence, the correct answer is 2744.
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