Given, diameter of sphere = 12 cm
then, radius of sphere (r)=122=6 cm
Volume of sphere = 43πr3
= 43×π×(6)3 cm3
Now, sphere is completely submerged in water and rise in water in cylindrical vessel is 359cm.
Volume of sphere = Volume of cylindrical vessel
43π×(6)3=πr2×329
r2=4×6×6×6×93×32
r=√81
r=9 cm
∴ Diameter of the cylindrical vessel is 18 cm.