Supposed a cylinder and a cone share the same radius and the same height which ratio describes the relationship between the formulas for the volume of a cone to the volume of cylinder
The ratio that describes the relationship between the formulas for the volume of a cone and the volume of a cylinder is 1:3.
The formula for the volume of a cone is given by V_cone = (1/3)πr^2h, where r is the radius and h is the height.
The formula for the volume of a cylinder is given by V_cylinder = πr^2h, where r is the radius and h is the height.
If the cone and the cylinder share the same radius and the same height, the ratio of their volumes can be obtained by dividing the volume of the cone by the volume of the cylinder:
V_cone / V_cylinder = ((1/3)πr^2h) / (πr^2h)
Simplifying the expression gives:
V_cone / V_cylinder = (1/3) / 1
Therefore, the ratio of the volume of the cone to the volume of the cylinder is 1:3.