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Question
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and `1/8` space of the cube remains unfilled. Number of marbles required is
Options
142296
142396
142396
142596
Solution
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and `1/8` space of the cube remains unfilled. Number of marbles required is 142296.
Explanation:
since `1/8` th of the cube remains unfulfilled,
volume of the cube `= 22xx22xx22 "cm"^3`
space filled in the cube `= (7/8xx22xx22xx22) "cm"^3`
= (7×1331) cm3
Radius of each marble `= 0.5/2 "cm"`
`=5/20 "cm"`
`= 1/4 "cm"`
Volume of each marble `= 4/3 pir^3`
`= (4/3 xx 22/7xx1/4xx1/4xx1/4) "cm"^3`
`= (11/24 xx 7) "cm"^3`
Therefore, number of marbles required `= ((7xx1331xx24xx7)/11)`
= 142296
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