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A hollow cube of internal edge $22$ cm is filled with spherical marbles of diameter $0.5$ cm and it is assumed that $18$ space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

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142296

142396

142496

142596

answer is A.

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Detailed Solution

Given that, internal edge of the hollow cube is 22cm.
The diameter of marbles is 0.5cm and,

18

space of the cube remains unfilled.
Determine the volume of a cube with side,

a = 22

cm and volume of sphere with radius,

d = 0.5

cm.

Volume of cube = a 3 = 223 = 10648 c m 3

Volume of sphere = 4 π 3 d 2 3 = 4 π 3 0.5 2 3 = 43227164 = 11168 c m 3

Determine the filled space of the cube by subtracting the

18

of the volume of the cube from the volume of the cube.

Filled volume = 10648 − 106488 = 10648 − 1331 = 9317 c m 3

Number of sphere = 931711168 = 931716811 = 142296

The number of marbles that the cube can accommodate is 142296.
Hence option 1) is correct.

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