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 of a cone $=r=5$ cm

Height of the cone $=h=24$ cm

Radius of the cylinder $=R=10$ cm

Height of the cylinder $=H=?$

Volume of water in conical vessel $=$ Volume in cylindrical vessel

$\Rightarrow \frac{1}{3}\pi r^{2}h=\pi R^{2}H$

$\Rightarrow \frac{1}{3}\pi 5^2\left(24\right)=\pi {10}^{2}H$

$\Rightarrow 200=100H$

$\therefore H=2$ cm.