Final answer:
To find the height of a cone with the same volume as a cylinder, use the formula for the volume of a cylinder, V = πr²h, and then solve for the height of the cone knowing that it is three times the height of the cylinder.
Step-by-step explanation:
The question pertains to finding the height of a cone given that it has the same volume as a cylinder. To solve this, we shall use the formula for the volume of a cylinder, which is V = πr²h. Knowing the volume of the cylinder, the volume of the cone can be expressed as ⅓ times the volume of the cylinder since the cone's volume is one third of a cylinder with the same base and height, V = ⅓πr²h. To find the height of the cone (h_cone), we equate the cone's volume to that of the cylinder and solve for h_cone, resulting in h_cone = 3h_cylinder, where h_cylinder is the height of the cylinder. Therefore, the height of the cone is three times the height of the cylinder with equal volume.