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

Let r be the radius of the base of a right circular cylinder and h be its height. The radius of a right circular cylinder's base is cut in half, and its height is doubled.

Volume of the cylinder $=\pi r^{2}h$

The height is doubled, keeping the radius the same.

Volume of the new cone $=\pi r^2\left(2h\right)=2\pi r^{2}h$

The ratio of the volume of the new cylinder to the original one is 2:1.