Suppose a cylinder and alone 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 volume of a cone is given by the formula V_cone = (1/3)πr^2h, where r is the radius and h is the height of the cone.
The volume of a cylinder is given by the formula V_cylinder = πr^2h, where r is the radius and h is the height of the cylinder.
In this case, the height of the cylinder is twice the radius, which means h = 2r.
Plugging this value of h into the volume formulas:
V_cone = (1/3)πr^2(2r)
V_cone = (2/3)πr^3
V_cylinder = πr^2(2r)
V_cylinder = 2πr^3
The ratio of the volume of the cone to the volume of the cylinder is given by:
(2/3)πr^3 : 2πr^3
Simplifying this ratio:
(2/3) : 2
The relationship between the formulas for the volume of a cone to the volume of a cylinder is 2:3.