Question

A conical container of base radius 'r' and height 'h' is full of water which is poured into a cylindrical container of radius mr then it will occupy a height equal to

• A. $3m^{2}h$
• B. $\frac{h}{3m^2}$
• C. $\frac{mh}{3}$
• D. $\frac{3h}{m}$

Answer 1

The correct option is B $\frac{h}{3m^2}$

Given base radius and height of conical container is r and h respt.

Then volume of conical container=$\frac{1}{3}\pi r^{2}hc{m}^3$

The conical container full of water which is poured into cylindrical container of radius mr

Then volume of cylindrical container=$\pi (mr{)}^{2}H$( where H is the height of cylindrical container)

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

Then height of cylindrical container=$\frac{h}{3m^2}$