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
A. radius of the cone = 15; height of the cone = 4
B. radius of the cone = 5; height of the cone = 4
C. radius of the cone = 15; height of the cone = 12
D. radius of the cone = 5; height of the cone = 12
To find the volume of a cylinder, you use the formula V = πr^2h, where r is the radius and h is the height. To find the volume of a cone, you use the formula V = (1/3)πr^2h.
Since the volumes of the cylinder and the cone are the same, we can set their volume formulas equal to each other:
πr^2h = (1/3)πr^2h
This simplifies to h = (1/3)h
Therefore, the height of the cone must be 1/3 of the height of the cylinder.
Looking at the options given:
A. radius of the cone = 15; height of the cone = 4
B. radius of the cone = 5; height of the cone = 4
C. radius of the cone = 15; height of the cone = 12
D. radius of the cone = 5; height of the cone = 12
The only option that satisfies the condition of the height of the cone being 1/3 of the height of the cylinder is option D: radius of the cone = 5; height of the cone = 12.
Therefore, the correct answer is D.