Suppose a sphere, cylinder, and cone all share the same radius and the cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
The formula for the volume of a sphere is $\frac{4}{3}\pi r^3$, where $r$ is the radius. The formula for the volume of a cylinder is $\pi r^2h$, where $r$ is the radius and $h$ is the height. The formula for the volume of a cone is $\frac{1}{3}\pi r^2h$, where $r$ is the radius and $h$ is the height.
Since the radius and the height are the same for the cylinder and the cone, their volume formulas are proportional by a factor of $1/3$, i.e., the volume of the cone is one-third of the volume of the cylinder.
On the other hand, the volume of the sphere is not proportional to the volume of the cylinder or the cone. Therefore, none of the given options state the correct relationship between the volume formulas.