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?
The volume of a cone is given by the formula 1/3 * π * r^2 * h, where r is the radius and h is the height.
The volume of a sphere is given by the formula 4/3 * π * r^3, where r is the radius.
In this case, the height of the cone is twice the radius, so h = 2r.
Substituting this value of h into the volume formula for the cone, we get V_cone = 1/3 * π * r^2 * 2r = 2/3 * π * r^3.
Therefore, the ratio between the volume of the cone and the volume of the sphere is: V_cone/V_sphere = (2/3 * π * r^3) / (4/3 * π * r^3) = 2/4 = 1/2.
So, the relationship between the formulas for the volume of a cone to the volume of a sphere is 1:2.