We have, 
Radius of the cylindrical vessel  = 30 cm
Radius of the sphere    = 15 cm
Volume of the sphere $=\frac{4}{3}\mathrm{\pi }\times (15{)}^3{\mathrm{cm}}^3$
Suppose water level rises by h cm in the cylindrical vesel, Then, volume of the cylinder of height h cm and  radius 30 cm = (π ×(30)² × h) cm³
Clearly, volume of the water displaced by the sphere is equal to the volume of the sphere
$\mathrm{\pi }\times (30{)}^2\times \mathrm{h}=\frac{4}{3}\mathrm{\pi }\times (15{)}^3$
$\mathrm{h}=\frac{\frac{4}{3}\mathrm{\pi }\times 15\times 15\times 15}{\mathrm{\pi }\times 30\times 30}$
h = 5 cm