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Question

A solid metal ball of radius 8 cm is melted and cast into smaller balls, each of radius 2 cm. The number of such balls is:


A
8
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B
16
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C
32
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D
64
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Solution

The correct option is D 64
Let we cast big ball into $$n$$ number of small balls.

Therefore,
Volume of big ball =n$$\times$$ Volume of small balls

$$\implies \dfrac{4}{3}\pi (8)^3=n(\dfrac{4}{3}\pi (2)^3)$$

$$\implies n=\dfrac{512}{8}=64$$

Hence the number of such balls is $$64$$.

Mathematics

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