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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