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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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135

125

140

130

answer is B.

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Detailed Solution

Given, radius of first sphere= 8 cm.
The radius of small lead balls

= 16 m m

.
We know 10 mm= 1cm.
So, 16mm=1.6cm.
We know, volume of a sphere

= 43 π r 3

.
Total number of possible small lead balls

= v o l u m e of 1st sphere v o l u m e of small lead balls

⇒ 43 π (8) 3 43 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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