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

1.	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» (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

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»

(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