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 = 5; height of the cone = 12 radius of the cone = 5; height of the cone = 12 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
To find the volume of a cylinder, you use the formula V = πr^2h, where r is the radius of the base and h is the height.
To find the volume of a cone, you use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.
Since the volume of the cone and the cylinder are equal, we can set the two volume formulas equal to each other and solve for the possible combinations of radius and height for the cone.
For the cylinder, V = πr^2h
For the cone, V = (1/3)πr^2h
Equating the two volumes:
πr^2h = (1/3)πr^2h
3πr^2h = πr^2h
3 = 1/3
This equation is not possible, so there is no combination of radius and height for the cone that would make its volume equal to the cylinder's volume.