Question

If the height of cylinder is halved keeping the radius constant , its volume will be

• A. $\frac{1}{2}$ times
• B. $\frac{1}{3}$ times
• C. $2$ times
• D. $3$ times

Answer 1

The correct option is A $\frac{1}{2}$ times

Let the initial radius $=r$
Initial height $=h$
Initial volume $=V_1=\pi r^{2}h$
Final height $=\frac{h}{2}$
Final volume $=V_2=\pi r^2\frac{h}{2}$
$\frac{V_2}{V_1}=\frac{\pi r^2\frac{h}{2}}{\pi r^{2}h}=\frac{1}{2}{V}_2=\frac{1}{2}{V}_1$
So the volume of the cylinder is halved.
Option $A$ is correct.