Given: Radius of the base of a right circular cylinder is halved, keeping the height the same.

Let initial Radius of Right Circular Cylinder be ‘r’.

∴ Radius of the Cylinder after its radius is halved is ‘ ’

Let ‘h’ be the height of the both the cylinders.

Let V₁ be the volume of the initial Cylinder.

Let V₂ be the volume of the Cylinder after the initial Cylinders base radius is halved.

Volume of the Cylinder is given by: πr²h

∴ V₁:V₂ = π(r₁)²h : π(r₂)²h

∴ V₁:V₂ = π(r)²h : π(r_/2)²h

⇒ V₁:V₂ = 1:

⇒ V₁:V₂ = 4:1

Thus, ratio of the volume of the cylinder thus obtained to the volume of original is 4:1.