Based on the given information that the cylinder and the cone have the same volume, we can use the formula for the volume of a cylinder and a cone to set up an equation to solve for the radius and height of the cone.
Let the radius of the cone be r and the height of the cone be h. The volume of a cylinder is given by V_cylinder = π(r^2)h, and the volume of a cone is given by V_cone = (1/3)π(r^2)h.
Given that the volume of the cylinder and the cone are equal, we can set up the following equation:
π(5^2)(4) = (1/3)π(r^2)h
Solving for r and h gives:
25(4) = (1/3)r^2h
100 = (1/3)r^2h
r^2 * h = 300
Now we can check each set of values:
1. r = 5; h = 4
5^2 * 4 = 100 (not equal to 300)
2. r = 15; h = 4
15^2 * 4 = 900 (equal to 300)
3. r = 15; h = 12
15^2 * 12 = 2700 (not equal to 300)
4. r = 5; h = 12
5^2 * 12 = 300 (equal to 300)
Therefore, the correct answer is:
radius of the cone = 5; height of the cone = 12
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)
Responses
radius of the cone = 5; height of the cone = 4
radius of the cone = 5; height of the cone = 4
radius of the cone = 15; height of the cone = 4
radius of the cone = 15; height of the cone = 4
radius of the cone = 15; height of the cone = 12
radius of the cone = 15; height of the cone = 12
radius of the cone = 5; height of the cone = 12
radius of the cone = 5; height of the cone = 12
1 answer