1. A metallic solid is made up of a solid cylindrical base with a solid cone on its top. The radius of the base of the cone is 5 cm. and the ratio of the height of the cylinder and the cone is 3:2. A cylindrical hole is drilled through the solid with height equal to 2/$$3^{rd}$$ of the height of solid. What should be the radius (in cm) of the hole so that the volume of the hole is 1/$$3^{rd}$$ of the volume of the metallic solid after drilling?
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