A hollow cube of internal edge 22cm is filled with spherical marbles of . . .

Question : A hollow cube of internal edge 22cm 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 

(A) 142296 

(B) 142396 

(C) 142496

(D) 142596

Doubt by Veer

Solution : 

Side of cube (a) = 22 cm 

Diameter of spherical marble (d) = 0.5 cm 
Radius of spherical marble (r)
= 0.5/2
= 5/20
=1/4 cm

Let number of marbles cube can accomodate be x

ATQ = 
Volume of Cube - Volume of empty space = x × Volume of each marble 
Volume of cube - ⅛ (Volume of cube) = x × Volume of each marble 

Volume of cube (1-⅛) = x × Volume of each marble 

⅞ Volume of cube = x × Volume of each marble