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A spherical copper ball of diameter $21 cm$ is melted and recast into cubes, each of side $1.5 cm .$ What is the number of cubes so formed and the copper left?

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1400,

1.125 cm 3

1437,

1.125 cm 3

1237,

2.225 cm 3

1437,

1.005 cm 3

answer is B.

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Detailed Solution

Given that a spherical copper ball of diameter

21 cm

and the side of cubes is 1.5cm.
We have the following formulae,
Volume of sphere =

43 π r 3

Volume of cube =

s 3

Volume of the sphere will be,

= 43 π r 3 = 43 π d 2 3 = 16 π (21) 3 = 16 × 227 × 9261 = 4851 cm 3

Volume of each cube will be,

= (1.5) 3 = 3.375 cm 3

Number of cubes formed will be,

= V o l u m e o f s p h e r e V o l u m e o f e a c h c u b e

= 4851 3.375 = 1437. 3 ¯ ≈ 1437

Amount of copper left = volume of sphere – volume of 1437 cubes

= 4851 − 1437 × (3.375)

= 4851 − 4849.875

= 1.125 cm 3

Thus, the no of cubes formed is 1437 and the amount of copper left is

1.125 cm 3

.
Therefore the correct option is 2.

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