Question 1178422


 the volume of a sphere is{{{ V = (4/3) pi*r^3}}}

if diameter of spherical balls {{{1.5cm}}}, radius is {{{r=1.5cm/2=0.75cm}}}


{{{V = (4/3) pi*(0.75cm)^3}}}

{{{V = 1.767145cm^3}}} 


a box measuring {{{6cm }}} by {{{3cm}}} by {{{3cm}}} has a volume

{{{V = 6cm*3cm*3cm}}}

{{{V = 54cm^3}}}


how many balls as possible are packed in the box: 

{{{54cm^3/1.767145cm^3}}}

={{{54/1.767145}}}

={{{30.56}}}

so, max is {{{30}}} balls


how much free space remains in the box:

find the volume of {{{30}}} balls and deduct from the volume of the box

{{{V = 30*1.767145cm^3}}}

{{{V = 53.01435cm^3}}}

{{{54cm^3-53.01435cm^3}}}

{{{0.9857cm^3}}}-> free space remains in the box