To find the volume of a cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.
The volume of the cylinder in this case is V_cylinder = π(10/2)^2 * 4 = 100π.
The volume of a cone is V_cone = 1/3 * πr^2h, where r is the radius and h is the height.
Since the cone and the cylinder have the same volume, we have:
V_cone = V_cylinder
1/3 * πr^2h = 100π
r^2h = 300
Since we don't know the height of the cone, let's express the radius in terms of the height:
r = √(300/h)
The radius of the cone could be any value that corresponds to the above equation. So, the possible values for the radius and height of the cone could be any pair that satisfies the equation r^2h = 300. For example, r = √75 and h = 4, or r = √150 and h = 2.
an image shows a cylinder with a height of 4 and width of 10, and a cone with no confirmed height or diameter.
If the cylinder and the cone in the image had the same volume, then the radius and height of the cone could be which of these?
1 answer