Question

A conical flask is full of water. The flask has base radius $3$cm and height $15$cm. The water is poured into cylindrical glass tube of uniform inner radius $1.5$cm, placed vertically and closed at lower end. Find the height of weight in the glass tube.

Answer 1

Volume of water in cone$=$ Volume of water in cylinder $\therefore \frac{1}{3}\pi r_c^2{h}_c=\pi r_{cy}^2{h}_{cy}$
$\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 15c{m}^3=\frac{22}{7}\times 1.5\times 1.5\times h_{cy}$
$\therefore h_{cy}=\frac{\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 15}{\frac{22}{7}\times 1.5\times 1.5}=20cm$
$\therefore$ Height of water in the glass tube$=20$cm