Question

conical flask is full of water. The flask has base-radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.​

Answer 1

$\huge\mathfrak{Answer:}$

GIVEN -

Radius of the conical flask = r

Height of the conical flask = h

Radius of the cylindrical flask = mr

TO FIND -

Height of the cylindrical flask = H

SOLUTION -

If water is poured from conical flask into the cylindrical flask then the volume of water remains the same in both

Therefore

volume of conical flask = volume of cylindrical flask

$\frac{1}{3} \pi \: {r}^{2} h = \pi {r}^{2}h$

$\frac{1}{3} \pi {r}^{2} h \: = \: \pi {(mr)}^{2} H$

$H = \frac{h}{3m {}^{2} }$

Hence the height of the cylindrical flask is

h/3m²