Q. 314.5( 2 Votes )
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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