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 of the volume of a cone to the volume of a cylinder
The volume of a cone is given by the formula V_cone = 1/3 * π * r^2 * h, where r is the radius and h is the height.
The volume of a cylinder is given by the formula V_cylinder = π * r^2 * h.
Given that the radius and height of both the cone and cylinder are the same (r and 2r respectively), we can substitute these values into the formulas:
V_cone = 1/3 * π * r^2 * 2r = 2/3 * π * r^3
V_cylinder = π * r^2 * 2r = 2π * r^3
Therefore, the ratio of the volume of a cone to the volume of a cylinder is:
V_cone : V_cylinder = 2/3 * π * r^3 : 2π * r^3
= 2/3 : 2
= 1 : 3
So, the relationship between the formulas of the volume of a cone and the volume of a cylinder is 1:3.