If a solid cone of volume 27π cm³ is kept inside a hollow cylinder whose radius and height are equal to that of the cone, then the volume of water needed to fill the empty space is

Volume of cone = $$\frac{1}{3}\pi {r^2}h$$
Volume of cylinder = $$\pi {r^2}h$$
Volume of water = Volume of cylinder - volume of cone
$$\eqalign{ & = \pi {r^2}h - \frac{1}{3}\pi {r^2}h \cr & = \frac{2}{3}\pi {r^2}h \cr & = 2\left( {\frac{1}{3}\pi {r^2}h} \right) \cr & = 2 \times 27\pi \cr & = 54\pi {\text{ c}}{{\text{m}}^3} \cr} $$