Suppose a sphere and a cone share the same radius and the height of the cone is twice the radius. Which ratio describes the relationship between the formulas for the volume of a cone to the volume of a sphere?(1 point):
The ratio is 1:3.
The formula for the volume of a cone is V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height. In this case, the height of the cone is twice the radius, so h = 2r.
Substitute h = 2r into the formula for the volume of a cone:
V_cone = (1/3) * π * r^2 * 2r = (2/3) * π * r^3
The formula for the volume of a sphere is V_sphere = (4/3) * π * r^3
Therefore, the ratio of the volume of a cone to the volume of a sphere is:
V_cone : V_sphere = (2/3) * π * r^3 : (4/3) * π * r^3
V_cone : V_sphere = 2 : 4
V_cone : V_sphere = 1 : 2
Since both volumes have the same radius, the final simplified ratio is 1:3.