Question

A conical flask is full of water. The flask has base radius $a$ and height $2a$. The water is poured into a cylindrical flask of base-radius $\frac{2a}{3}$. Find the height of water in the cylindrical flask.

• A. $\frac{5}{2}a$
• B. $2a$
• C. $\frac{3}{2}a$
• D. $1a$

Answer 1

The correct option is C $\frac{3}{2}a$

Volume of water in the conical flask will be equal to the volume of water in the cylindrical flask.
Volume of a cylinder $=\pi R^{2}h$
Volume of a cone $=\frac{1}{3}\pi r^{2}h$

where, $r$ is the radius of the base of the cone and $h$ is the height.
Hence, $\frac{22}{7}\times {\left(\frac{2a}{3}\right)}^2\times h=\frac{1}{3}\times \frac{22}{7}\times a^2\times 2a$
$h=\frac{3}{2}a$ cm
Hence, height of water in the cylindrical flask is $\frac{3}{2}a$ cm.