A geometry problem by vishwathiga jayasankar

The volume of the sphere must be equal to the volume of the wire.

$\dfrac{4}{3} \pi R^3 = \pi r^2 L$

$\dfrac{4}{3} \pi 9^3 = \pi r^2 (108)$

$972=108r^2$

$r^2=9$

$r=3$

So the desired diameter is $2r=2(3)=6~cm$