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The volume formulas for the sphere, cylinder, and cone are as follows:
- Sphere: V = (4/3)Ï€r^3
- Cylinder: V = πr^2h = πr^2(2r) = 2πr^3
- Cone: V = (1/3)Ï€r^2h = (1/3)Ï€r^2(2r) = (2/3)Ï€r^3
Therefore, the relationship between the volume formulas for the sphere, cylinder, and cone is as follows:
V_sphere : V_cylinder : V_cone = (4/3)Ï€r^3 : 2Ï€r^3 : (2/3)Ï€r^3 = 4 : 6 : 2
Hence, the relationship between the volume formulas for the sphere, cylinder, and cone is 4:6:2.