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

Let the radius of the cylinder is r and height is h
∴Volume of the cylinder = πr²h
According to the question new radius is half of the initial radius
∴New radius=r/2
Height is h.
∴New volume of the cylinder = π(r/2)²h = πr²/4h
∴The ratio of the new volume of the cylinder and initial volume of the original cylinder = πr²/4h / πr²h = 1/4
∴Ratio=1:4.