Final answer:
The volume of the cylinder is greater than the volume of the cone.
Step-by-step explanation:
The relationship between the volume of the cylinder and the cone can be determined by comparing their formulas for volume. The volume of the cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The volume of the cone is given by the formula V = (1/3)πr²h, where r is again the radius and h is the height.
In this case, the diameter of both the cylinder and the cone is 8 inches, so the radius is half of that, which is 4 inches. Given that the height of the cylinder is 9 inches and the height of the cone is 18 inches, we can now calculate the volumes of both shapes.
For the cylinder, using the formula V = πr²h, we have V = 3.14 × (4 inches)² × 9 inches ≈ 452.16 cubic inches.
For the cone, using the formula V = (1/3)πr²h, we have V = (1/3) × 3.14 × (4 inches)² × 18 inches ≈ 301.44 cubic inches.
Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cylinder is greater than the volume of the cone.