Question

The $\frac{3}{4}$th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Answer 1

Radius of conical vessel r = 5 cm

Height of conical vessel h = 24 cm

The volume of water = $\frac{3}{4}\times$volume of conical vessel.
$$\begin{gathered} =\frac{3}{4}\times \frac{1}{3}\pi r^{2}h \\ =\frac{3}{4}\times \frac{1}{3}\pi \times 25\times 24 \\ =150\mathrm{\pi } \end{gathered}$$

Let h' be the height of cylindrical vessel, which filled by the water of conical vessel,

Radius of cylindrical vessel = 10 cm

Clearly,

Volume of cylindrical vessel = volume of water
$$\begin{gathered} \pi {\left(10\right)}^{2}h=150\pi \\ \Rightarrow h=\frac{150\pi }{100\pi } \\ \Rightarrow h=1.5\mathrm{cm} \end{gathered}$$

Thus, the height of cylindrical vessel is 1.5 cm.