Question

If the radius of the base of a right circular cylinder is halved keeping the height same, what is the ratio of the volume of the volume of the reduced cylinder to that of the original one ?

• A. $1:4$
• B. $1:8$
• C. $1:2$
• D. $8:1$

Answer 1

The correct option is A $1:4$

Let the radius of the original cylinder $=r$ cm and height $=h$ cm
Original volume $=\pi r^{2}h$
New Radius after decrease $=\frac{r}{2}$
Now, new volume of the cylinder $=\pi \times {\frac{r}{2}}^{2}timesh=\frac{\pi r^2}{4}h$
Required ratio $=\frac{Newvolume}{Originalvolume}=\frac{\frac{\pi r^2}{4}h}{\pi r^{2}h}=1:4$