Rise in Water Level in Cylinder

Volume of water displaced = Volume of sphere = $\frac{4}{3} \pi (3)^3 = 36\pi$. Rise in water level $h$ in cylindrical vessel of radius $r = 4$ cm: $\pi r^2 h = 36\pi \implies 16 \pi h = 36\pi \implies h = \frac{36}{16} = \frac{9}{4}$ cm.

Hence, Option C is correct.