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

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
(b) 16
(c) 32
(d) 64

 

Solution:

(d) 64

Number of balls $=\frac{\text { volume of solid metal ball }}{\text { volumeof } 1 \text { small ball }}$

$=\frac{\frac{4}{3} \pi \times 8^{3}}{\frac{4}{3} \pi \times 2^{3}}=\frac{512}{8}=64$

 

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