If 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 accommodate is

Options

A. 142244
B. 142344
C. 142444
D. 142544

Answer

A

Explanation

Given , edge of the cube = 22 cm
`therefore` Volume of the cube `= (22)^(3) = 10648 cm^(3) " "[because "Volume of cube " = ("Side")^(3)]`
Also, given diameter of marble = 0.5 cm
`therefore` Radius of a marble, `r = (0.5)/(2) = 0.25 cm" " [because diameter = 2 xx radius]`
volume of one marble `= (4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx (0.25)^(3)" "[therefore " Volume of sphere " (4)/(3) xx pi xx ("radius")^(3)]`
`= (1.375)/(21) = 0.0655 cm^(3)`
Filled space of cube = Volume of the cube `(1)/(8) xx ` volume of cube
`= 10648-10648 xx (1)/(8)`
`= 10648 xx (7)/(8) = 9317 cm^(3)`