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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