The radius of a cylinder is doubled and its height is halved; then the new volume is :

1. same

2. 2 times

3. 4 times

4. 8 times

Let r be the radius and h be the height of original cylinder.

It is given that radius of cylinder is doubled and its height is halved.

Thus, radius of new cylinder = 2r and height = $\dfrac{1}{2}h$

As we know, the volume of cylinder = πr²h

Volume of original cylinder $= \dfrac{22}{7}r^2h$

Volume of new cylinder:

$= \dfrac{22}{7} \times (2r)^2 \times \dfrac{1}{2}h\\[1em] = \dfrac{22}{7} \times 4r^2 \times \dfrac{1}{2}h\\[1em] = \dfrac{4}{2} \times \dfrac{22}{7}r^2h\\[1em] = 2 \times \dfrac{22}{7}r^2h$

The new volume is 2 times the original volume.

Hence, option 2 is the correct option.