A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is ______.

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A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is 142296. Explanation: According to the question, Volume of cube = 223 = 10648 cm3 Volume of cube that remains unfilled = $\frac{1}{8}$ xx 10648 = 1331 cm3 Volume occupied by spherical marbles = 10648 − 1331 = 9317 cm3 Radius of the spherical marble = 0.$\frac{5}{2}$ = 0.25 cm = $\frac{1}{4}$ "cm" Volume of 1 spherical marble = `$\frac{4}{3}$ xx $\frac{22}{7}$ xx ($\frac{1}{4}$)^3 = $\frac{11}{168}$ "cm"^3` Numbers of spherical marbles, n = 9317 xx ($\frac{11}{168}$) = 142296

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