Question

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

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

Answer 1

Answer: (A)

$142296$

Given, diameter $d=0.5$ cm

$\therefore$ radius $r=0.25$cm

$x$ =no. of marbles.
Volume of cube$=($edge${)}^3$
Volume of sphere $=\frac{4}{3}\pi r^3$
$\Rightarrow \left(10648\right)-$${\frac{1}{8}}^{th}$ of $(22{)}^3=\frac{4}{3}\pi r^{3}x$
$\Rightarrow (10648-1331)=\left(\frac{4\left(22\right)\left({0.25}^3\right)}{\left(3\right)\left(7\right)}\right)x$
$\Rightarrow \left(9317\right)=\left(0.06547\right)x$
$\Rightarrow x=142296$