suppose a sphere and a cone share the same radius and the same height of the cone is twice the radius. which ratio describes the relationship between the formulas of the volume of a cone to the volume of a sphere
The volume of a cone is $\frac{1}{3}\pi r^2 h$ and the volume of a sphere is $\frac{4}{3}\pi r^3$.
Given that the height of the cone is twice the radius, we can substitute $h = 2r$ into the cone volume formula to get:
$\frac{1}{3}\pi r^2 (2r) = \frac{2}{3}\pi r^3$
Therefore, the ratio of the volume of the cone to the volume of the sphere is $\frac{2}{3}$.