10 diameter
4 height
If the cylinder and the cone shown have the same volume, then the radius and height of the cone could be which of these? (2 points)
radius of the cone = 15; height of the cone = 4
radius of the cone = 5; height of the cone = 4
radius of the cone = 5; height of the cone = 12
radius of the cone = 15; height of the cone = 12
To find the volume of a cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the cylinder is 10, the radius is 5. The height of the cylinder is 4.
The volume of the cylinder is V_cylinder = π(5)^2 * 4 = 100π.
To find the volume of a cone, we use the formula V = 1/3 * πr^2h.
Let's check the volume of the cone for each set of radius and height values:
1. radius of the cone = 15; height of the cone = 4
V_cone = 1/3 * π(15)^2 * 4 = 300π. This set of values does not match the volume of the cylinder.
2. radius of the cone = 5; height of the cone = 4
V_cone = 1/3 * π(5)^2 * 4 = 100π. This set of values matches the volume of the cylinder.
3. radius of the cone = 5; height of the cone = 12
V_cone = 1/3 * π(5)^2 * 12 = 240π. This set of values does not match the volume of the cylinder.
4. radius of the cone = 15; height of the cone = 12
V_cone = 1/3 * π(15)^2 * 12 = 900π. This set of values does not match the volume of the cylinder.
Therefore, the correct answer is:
radius of the cone = 5; height of the cone = 4