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


Given,


Internal edge of cube, a = 22 cm


As we know,


Volume of cube = a3,


where a = side of cube, we have


Volume of given hollow cube = a3


= (22)3 = 10648 cm3


As of the cube remains unfilled, only of cube remains filled


Volume of Filled cube = 7/8 of total volume = 7/8×10648 = 9317 cm3


Now,


Diameter of marble, D = 0.5 cm


Radius of marble, r = D/2 = 0.5/2 = 0.25 cm


Volume of one marble = volume of sphere of radius r


Volume of one marble,


[As volume of sphere





No of total marbles


No. of marbles


= 142,244.275


= 142,244 (appx)

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