Final answer:
The volume of a cone is one-third of the volume of a cylinder when the radii and heights are equal.
Step-by-step explanation:
The relationship between the volume of a cone and a cylinder when the radii and heights are equal is that the volume of the cone is exactly one-third of the volume of the cylinder.
To understand this relationship, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. For a cylinder with equal radius and height, the formula for the volume is V = πr^2h. By comparing the two formulas, we can see that the volume of the cone is one-third of the volume of the cylinder.
For example, if the radius and height of both the cone and cylinder are 4 units, the volume of the cone would be (1/3)π(4^2)(4) = 67.03 cubic units, while the volume of the cylinder would be π(4^2)(4) = 201.06 cubic units. Therefore, the volume of the cone is one-third of the volume of the cylinder.