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assuming you mean a sphere (because cone and cylinder requires height)
V=(4/3)pir^3
when V=pir, find r
pir=(4/3)pir^3
divide both sides by pir
1=(4/3)r^2
times both sides by 3/4
3/4=r^2
sqrt both sides
[tex] \frac{ \sqrt{3} }{2} [/tex]=r
the radius would have to be [tex] \frac{ \sqrt{3} }{2} [/tex] units
