How does the volume of a cylinder change when its diameter is halved

The volume of a cylinder is given by πr²h where, r is the radius of the cylinder and h is the height of the cylinder.

Also r=d/2, where d is the diameter of the cylinder.

Therefore if the diameter is halved, the radius also gets halved, i. e., it becomes r/2. Therefore the new volume = π (r/2) ²h

=π (r²/4) h

= (1/4) πr²h