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

Options

A. 142296
B. 142396
C. 142496
D. 142596

Answer

A

Explanation

Space filled in the cube `=(7/8 xx 22xx 22 xx 22)cm ^2=(7 xx 1331)cm^3`
Radius of each marble `=(0.5)/(2) cm =(5)/(20) cm =1/4 cm .`
Volume of each marble `=(4/3 pi r^3=(4/3xx 22/7 xx 1/4xx1/4xx 1/4)cm^3 =((11)/(24xx7))cm^3`
Number of marbles `=4/3 pi r^3=(4/3 xx 22/7 xx 1/4 xx 1/4 xx 1/4 ) cm^3 =((11)/(24 xx 7) cm^3`
Number of marbles `=((7xx 1313 xx 24xx 7)/(11))=142296 `