A conical vessel whose internal base radius is 18 cm and height 60 cm is full of a liquid. The entire liquid of the vessel is emptied into a cylindrical vessel with internal radius 15 cm. The height (in cm) to which the liquid rises in the cylindrical vessel is: 

28.8 cm

We know that,

Volume of cylinder = πr²h

Volume of cone = \(\frac{1}{3}\) πr²h

Volume of cone = \(\frac{1}{3}\) × π × 18² × 60 = π × 6480

According to the question,

The internal radius of the cylindrical vessel = 15 cm

Let the height = H

We know that,

Volume of cylinder = π × 15² × H

According to the question,

Volume of cone = Volume of cylinder

= π × 6480 = π × 15² × H

H = \(\frac{6480}{225}\) = 28.8 cm