<PRE><B>Question 1189050</B>
A sphere is placed in a cubical container in such way that the faces of the container are tangent to the sphere. The remaining space of the container is filled with one kilogram of water. What is the radius of the sphere? 
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1 kg of water is a volume of 1000 cc
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r = radius of the sphere.  Its volume is {{{4pi*r^3/3}}} cc
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The volume of the cube is (2r)^3 = 8r^3
The space filled by water is {{{8r^3 -4pi*r^3/3}}}
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{{{8r^3 -4pi*r^3/3 = 1000}}}
{{{24r^3 - 4pi*r^3 = 3000}}}
{{{r^3 = 3000/(24 - 4pi)}}}
{{{r^3 = 262.38}}}  apx
r =~ 6.4 cms</PRE>