Suppose a cylinder and a cone share the same radius and the same height which is twice the radius which ratio describes the relationship between the formulas for the volume of a cone to the volume of a cylinder

The ratio between the volume of a cone and the volume of a cylinder with the same radius and height is 1:3. This is because the volume of a cone is one third the volume of a cylinder with the same base area and height. The formula for the volume of a cone is given by V = (1/3)πr^2h, while the formula for the volume of a cylinder is given by V = πr^2h.