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 accommodate is

(A) 142296 (B) 142396

(C) 142496 (D) 142596

Answer 1

(A) 142296

According to the question,

Volume of cube =22³=10648cm³

Volume of cube that remains unfilled =1/8×10648=1331cm³

volume occupied by spherical marbles =10648−1331=9317cm³

Radius of the spherical marble = 0.5/2=0.25cm=1/4cm

Volume of 1 spherical marble = 4/3×22/7 × (1/4)³=11/168cm³

Numbers of spherical marbles, n = 9317 × (11/168) =142296