A sphere of radius 6 cm is dropped into a cylindrical vessel, partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by :

1. 2 cm

2. 3 cm

3. 4 cm

4. 4.5 cm

Radius of sphere, r = 6 cm

Radius of cylinder, R = 8 cm

Let the rise in water level be x cm.

∴ Volume of water that rises by x cm in the cylindrical vessel = Volume of sphere submerged

$\Rightarrow π\text{R}^2\text{x} = \dfrac{4}{3} π\text{r}^3 \\[1em] \Rightarrow 8^2\text{x} = \dfrac{4}{3} \times 6^3 \\[1em] \Rightarrow 64\text{x} = \dfrac{4}{3} \times 216 \\[1em] \Rightarrow 64\text{x} = 4 \times 72 \\[1em] \Rightarrow 64\text{x} = 288 \\[1em] \Rightarrow \text{x} = \dfrac{288}{64} \\[1em] \Rightarrow \text{x} = 4.5 \text{ cm.}$

Hence, option 4 is the correct option.