# 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 isA. 142296B. 142396C. 142496D. 142596

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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