Question

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use $\pi =\frac{22}{7}$)

Answer 1

Given, radius (r) and height (h) of conical vessel is 5 cm and 24 cm respectively.

Volume of water in conical vessel = $\frac{1}{3}\pi r^{2}h$

= $\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 24$

= $\frac{13200}{21}c{m}^3$

Since water is emptied into a cylindrical vessel.

Now, Volume of water in conical vessel = Volume of water in cylindrical vessel

$\frac{13200}{21}=\pi R^{2}H$

$\frac{13200}{21}=\frac{22}{7}\times 10\times 10\times H$

$H=\frac{13200\times 7}{21\times 22\times 10\times 10}$

$H=2cm$

$\therefore$ Height of water rise in cylindrical vessel is 2 cm.