Question

A conical container of base radius ${}^{\prime }{r}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$ is full of water which is poured into a cylindrical container of radius $r$, then it will occupy a height equal to

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

Answer 1

Answer: (C)

$\frac{h}{3}$

Given the base radius and height of a conical container is $r$ and $h$ respectively.

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

The conical container full of water which is poured into a cylindrical container of radius $r$

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

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

Hence, the height of cylindrical container=$\frac{h}{3}$.