A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water.

Solution:

Radius of the sphere = 6 cm.

Volume of the sphere

$=\frac{4}{3} \pi r^{3}$'

$=\frac{4}{3} \pi \times 6 \times 6 \times 6$

and

Radius of the cylinder = 8 cm

Volume of the cylinder

$=\pi r^{2} h$

$=\pi \times 8 \times 8 \times h$

Therefore,

Volume of the sphere = volume of the cylinder

$\frac{4}{3} \pi(6)^{3}=\pi(8)^{2} h$

or

$h=\frac{4 \times 72}{64}=4.5 \mathrm{~cm}$

Hence, the correct answer is choice (a).