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.