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Q.

A spherical lead ball of radius 8 cm   is melted and small lead balls of radius 16 mm   are made. The total number of possible small lead balls is,

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a

135

b

125

c

140 

d

130

answer is B.

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Detailed Solution

Given, radius of first sphere= 8 cm.
The radius of small lead balls =16mm  .
We know 10 mm= 1cm.
So, 16mm=1.6cm.
We know, volume of a sphere = 4 3 π r 3  .
Total number of possible small lead balls = volume of 1st sphere volume of small lead balls      ⇒ 4 3 π (8) 3 4 3 π (1.6) 3    ⇒ 8×8×8 1.6×1.6×1.6    ⇒ 8×8×8×1000 16×16×16      ⇒  125  Hence, there are 125 small lead balls.
Therefore, the correct option is 2.
 
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