Supposed to send in a cone, share the same radius in the same height, which is twice the radius. Which ratio describes the relationship between the formulas for the volume of the cone of the cylinder.
The ratio that describes the relationship between the formulas for the volume of the cone and the cylinder is 1:3.
The volume of a cone can be calculated using the formula: V_cone = (1/3)πr^2h
where r is the radius of the cone and h is the height.
The volume of a cylinder can be calculated using the formula: V_cylinder = πr^2h
where r is the radius of the cylinder and h is the height.
In the given scenario, the height of the cone is twice the radius, so we can substitute h = 2r in both formulas.
For the cone, the volume becomes: V_cone = (1/3)πr^2(2r) = (2/3)πr^3
For the cylinder, the volume remains the same: V_cylinder = πr^2(2r) = 2πr^3
Taking the ratio of the volume of the cone to the volume of the cylinder:
(2/3)πr^3 : 2πr^3 = 1 : 3
Therefore, the ratio that describes the relationship between the formulas for the volume of the cone and the cylinder is 1:3.