Question

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 ______.

पर्याय

• 142296

• 142396

• 142496

• 142596

Answer 1

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 142296.

Explanation:

Since `1/8` th of the cube remains unfulfilled,

Volume of the cube `= 22xx22xx22  "cm"^3`

Space filled in  the cube `= (7/8xx22xx22xx22) "cm"^3`

= (7 × 1331) cm³

Radius of each marble `= 0.5/2  "cm"`

`=5/20  "cm"`

`= 1/4 "cm"`

Volume of each marble `= 4/3 pir^3`

`= (4/3 xx 22/7xx1/4xx1/4xx1/4) "cm"^3`

`= (11/24 xx 7) "cm"^3`

Therefore, number of marbles required `= ((7xx1331xx24xx7)/11)`

= 142296