Question : The number of balls, each one is 4 cm in the diameter that can be made from a solid metallic sphere of diameter 32 cm is:
Option 1: 256
Option 2: 64
Option 3: 512
Option 4: 1024
Correct Answer: 512
Solution :
Let $n$ be the number of balls made.
Given,
The radius of new spherical balls (r) = 2 cm
The radius of the bigger ball (R) = 16 cm
Volume of bigger ball = n(Volume of smaller balls)
⇒ $\frac43\pi R^3=n(\frac43\pi r^3)$
⇒ $16\times16\times16=n\times2\times2\times2$
$\therefore n = 512$
Hence, the correct answer is 512.
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