A conical vessel whose internal base radiusis 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 theliquid rises in the cylindrical vessel is:

Conical vessel volume = $$\dfrac{1}{3}\pi r^2 h$$ where r = 18 cm and h = 60cm 

$$\Rightarrow\dfrac{1}{3}\pi (18)^2\times60cm^2 $$

and cylindrical vessel volume =$$\pi r^2 h = \pi(15)^2 h where r = 15 

so volume of conical  = volume of cylindrical then

$$\Rightarrow \dfrac{1}{3} (18)^2 \times 60 = \pi \times 15\times 15 h $$

$$\Rightarrow h = \dfrac {324\times 20}{225}$$

$$\Rightarrow h = 28.8 cm Ans $$