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)
To find the ratio between the volume of a cone and the volume of a sphere, we need to determine their respective formulas.
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h
where r is the radius and h is the height of the cone.
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
Since the radius of the cone is the same as the radius of the sphere, we can substitute r in the cone's formula with r in the sphere's formula.
V_cone = (1/3) * π * r^2 * (2r) = (2/3) * π * r^3
Now we can find the ratio between the volume of the cone and the volume of the sphere:
Ratio = (V_cone) / (V_sphere) = ((2/3) * π * r^3) / ((4/3) * π * r^3)
The π, r^3, and (3/3) terms cancel out, leaving us with:
Ratio = 2/4 = 1/2
Therefore, the ratio describing the relationship between the volume of a cone to the volume of a sphere is 1:2.