If the radius of a cylinder is doubled and the height is halved, what will be the ratio of the new volume to the previous volume?

Correct option is A

Given:

The radius of the cylinder is doubled.

The height of the cylinder is halved.

Formula Used:
The volume of a cylinder is given by the formula

V $$= \pi r^2 h$$ , where: r = radius of the base and h = height of the cylinder

Solution:

If the radius is doubled and the height is halved, the new radius becomes 2r and the new height becomes $$\frac{h}{2}.$$​
First, simplify the expression for the new volume:

​$$V_{\text{new}} = \pi (2r)^2 \times \frac{h}{2} = \pi \times 4r^2 \times \frac{h}{2} = 2 \pi r^2 h$$​​

Now, the original volume is:​$$V_{\text{original}} = \pi r^2 h$$

Thus, the ratio is:

​$$\frac{V_{\text{new}}}{V_{\text{original}}} = \frac{2 \pi r^2 h}{\pi r^2 h} = 2$$​​

The ratio of the new volume to the previous volume is 2:1.