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Question
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that `1/8` space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is ______.
Options
142296
142396
142496
142596
Solution
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that `1/8` space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is 142296.
Explanation:
According to the question,
Volume of cube = 223 = 10648 cm3
Volume of cube that remains unfilled = `1/8 xx 10648` = 1331 cm3
Volume occupied by spherical marbles = 10648 − 1331 = 9317 cm3
Radius of the spherical marble = `0.5/2` = 0.25 cm = `1/4 "cm"`
Volume of 1 spherical marble = `4/3 xx 22/7 xx (1/4)^3 = 11/168 "cm"^3`
Numbers of spherical marbles, n = `9317 xx (11/168)` = 142296
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