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I hope this will help you.
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let the side of the cube be a and the radius of the sphere be r.
therefore,
6a^2=4 pi r^2
2a^2=4/3 pi r^2
2a^2*r=4/3 pi r^3
the ratio of their volumes=a^3/4/3pir^3
=a^3/2a^2^r
=a/2r
a/D
therefore,
6a^2=4 pi r^2
2a^2=4/3 pi r^2
2a^2*r=4/3 pi r^3
the ratio of their volumes=a^3/4/3pir^3
=a^3/2a^2^r
=a/2r
a/D
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