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 = 12 radius of the cone = 5; height of the cone = 12 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 = 12 radius of the cone = 15; height of the cone = 12 radius of the cone = 15; height of the cone = 4
To find the volume of a cylinder, you use the formula V = πr^2h, where r is the radius and h is the height. The volume of a cone is given by V = (1/3)πr^2h.
Since the two shapes have the same volume, we can set their volume formulas equal to each other:
πr^2h = (1/3)πr^2h
This simplifies to:
3h = h
This means that the height of the cone must be three times the height of the cylinder. Looking at the given options, the correct answer would be:
Radius of the cone = 5; height of the cone = 4
Because when h = 4, 3h = 12, which matches the height of the cylinder.