Radius of cylinder = 12 cm
Height of cylinder = 6.75 cm
Volume of water = πr^{2}h
= π × 12 × 12 × 6.75 cm^{3}
Let the radius of iron sphere piece = R cm
∵ Volume of sphere = Volume of water
4/3πR^{3} = π × 12 × 12 × 6.75
R^{3 }= (π × 12 × 12 × 6.75 × 3)/4π
R^{3 }= 729
R = ^{3}√729 = 9 cm
Hence, the radius of sphere piece = 9 cm.