If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

$( A)$ 1:2
$( B)$ 2:1
$( C)$ 1:4
$( D)$ 4:1

Given: Radius of a cylinder is halved.

To do: To find out the ratio of the volume of the newly obtained cylinder to the volume of the original cylinder. 

Solution: let us say radius of original cylinder is $r$ and height off the original cylinder is $h$.

After reducing the radius of the cylinder to half,

Radius of newly obtained cylinder becomes $\frac{r}{2}$

Height of the newly obtained cylinder will remain the same $h$.

The volume of original cylinder is $ V1\ =πr^{2} h$

and the volume of newly obtained cylinder $ V_{2} =π\left(\frac{r}{2}\right)^{2} h=\frac{πr^{2} h}{4}$ 

$\therefore$ Ratio of the volumes of newly obtained and the original cylinder$=\frac{V_{1}}{V_{2}}$

$=\frac{\frac{πr^{2} h}{4}}{πr^{2} h}$ 

$=\frac{1}{4}$

Thus, Ratio of the volumes of newly obtained and the original cylinder$=V_{1}\ :\ V_{2}=1:4$

$\therefore$ Option $( C)$ is correct.
 

Updated on: 10-Oct-2022

52 Views

Related Articles

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements