Suppose a sphere, cylinder, and cone all share the same radius. 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?
The volume formula for a sphere is $\frac{4}{3}\pi r^3$ where $r$ is the radius. The volume formula for a cylinder is $\pi r^2 h$ where $h$ is the height and $r$ is the radius. The volume formula for a cone is $\frac{1}{3}\pi r^2 h$.
Since the cylinder and cone share the same radius $r$ and height $h$, their volume formulas can be written as $\pi r^2 h$ for the cylinder and $\frac{1}{3}\pi r^2 h$ for the cone.
Comparing the three formulae, we see that the volume of the sphere is $\frac{4}{3}$ times the volume of the cylinder (or the cone).
Therefore, the correct answer is $\boxed{\text{The volume of the sphere is }\frac{4}{3}\text{ times the volume of the cylinder (or the cone).}}$