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)
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Let's denote the radius of the sphere and the cone as r, and the height of the cone as h. According to the given information, the height of the cone is twice the radius, so h = 2r.
The formula for the volume of a sphere is V_s = (4/3)πr^3.
The formula for the volume of a cone is V_c = (1/3)πr^2h.
Substituting h = 2r into the formula for the volume of a cone, we get V_c = (1/3)πr^2(2r) = (2/3)πr^3.
The ratio between the volume of a cone and the volume of a sphere is V_c/V_s = (2/3)πr^3 / (4/3)πr^3.
Simplifying the ratio, we get V_c/V_s = 2/4 = 1/2.
Therefore, the ratio that describes the relationship between the formulas for the volume of a cone to the volume of a sphere is 1/2.