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

Solution (By Examveda Team)

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