Final answer:
The volume of the cylinder is three times greater than the volume of the cone when the diameter is the same and the cone's height is three times the height of the cylinder.
Step-by-step explanation:
To find the relationship between the volume of a cylinder and a cone with the same diameter and using π=3.14, we need to use the formulas for the volume of a cylinder and the volume of a cone.
Cylinder Volume
The volume of a cylinder (Vcyl) is calculated using the formula V = πr²h. With a diameter of 8 inches, the radius (r) is half of that, which is 4 inches. The height (h) is given as 5 inches. So the volume will be:
Vcyl = π * (4 in)2 * 5 in = 3.14 * 16 in2 * 5 in = 251.2 in3
Cone Volume
For a cone with the same diameter and using the same value for π, the volume (Vcone) is calculated using the formula V = (1/3)πr²h. The height of the cone is 15 inches, thus:
Vcone = (1/3) * π * (4 in)2 * 15 in = (1/3) * 3.14 * 16 in2 * 15 in = 251.2 in3
As we can see, the volume of the cylinder is exactly three times greater than the volume of the cone when they have the same diameter and when the height of the cone is three times the height of the cylinder, as π and the squared radius cancel out, and the remaining factor for the cone's volume is (1/3).