A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and 1/8 space of the cube remains unfilled. Number of marbles required is

Given: hollow cube of internal edge 22 cm


Spherical marbles of diameter 0.5 cm radius = = 0.25 cm


space of the cube remains unfilled.


Here, space of the cube is unfilled, that is of the cube is filled with marbles of radius 0.25cm.


Volume of the sphere is : × π × r3 (where ‘r’ is the radius of the cube)


Let V1 be the volume of the Sphere.


V1 = × π × (0.25)3 = cm3


Volume of the Cube : a3 (where ‘a’ is the edge length of the cube)


Let V2 be the volume of the cube.


V1 = (22)3 = 10648 cm3


Let ‘n’ be the number of sphere required to fill the space of the cube.


n × V1= V2 ×


n × = 10648 ×


n × = 9317


n = 9317 × = 142296


Number of marbles required to fill of the cube id 142296.

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