Question

A hollow cube of internal edge 22 cm 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 ______.

Options

• 142296

• 142396

• 142496

• 142596

Answer 1

A hollow cube of internal edge 22 cm 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 142296.

Explanation:

According to the question,

Volume of cube = 22³ = 10648 cm³

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

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

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

Volume of 1 spherical marble = `4/3 xx 22/7 xx (1/4)^3 = 11/168 "cm"^3`

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