A tool comprising an interchangeable cutting member and an adapter to which said interchangeable cutting member is adapted to be replaceably mounted; wherein: the interchangeable cutting member comprises a substantially ball-shaped body with a cutting surface, within which a female screw-thread is provided; the adapter is provided with a male screw-thread portion configured and arranged for screw-engagement in the female screw-thread; at least one coolant or lubricant fluid passage is provided in the interchangeable cutting member, said coolant or lubricant fluid passage ending at the cutting surface of the substantially ball-shaped cutting member; a coolant or lubricant fluid delivery duct is provided in the adapter, said coolant or lubricant fluid delivery duct being in fluid communication with said coolant or lubricant fluid passage when the interchangeable cutting member and the adapter are screwed together; the adapter is provided with a first convex conical surface, formed on a terminal portion of the adapter, and with a first axial abutment surface; and the interchangeable cutting member is provided with a second concave conical surface, formed in the interchangeable cutting member, and with a second axial abutment surface; characterized in that the male screw-thread portion projects from the first convex conical surface, formed on the terminal portion of the adapter; and the female screw-thread extends from a bottom of the concave conical surface formed in the interchangeable cutting member; wherein the first convex conical surface and the second concave conical surface are configured and arranged for mutually centering said adapter and said interchangeable cutting member, when the adapter and the interchangeable cutting member are screwed together; and wherein said first axial abutment surface and said second axial abutment surface are mutually engageable for axially positioning the interchangeable cutting member and the adapter one with respect to the other when said interchangeable cutting member and said adapter are screwed together. the interchangeable cutting member comprises a substantially ball-shaped body with a cutting surface, within which a female screw-thread is provided; the adapter is provided with a male screw-thread portion configured and arranged for screw-engagement in the female screw-thread; at least one coolant or lubricant fluid passage is provided in the interchangeable cutting member, said coolant or lubricant fluid passage ending at the cutting surface of the substantially ball-shaped cutting member; a coolant or lubricant fluid delivery duct is provided in the adapter, said coolant or lubricant fluid delivery duct being in fluid communication with said coolant or lubricant fluid passage when the interchangeable cutting member and the adapter are screwed together; the adapter is provided with a first convex conical surface, formed on a terminal portion of the adapter, and with a first axial abutment surface; and the interchangeable cutting member is provided with a second concave conical surface, formed in the interchangeable cutting member, and with a second axial abutment surface; characterized in that the male screw-thread portion projects from the first convex conical surface, formed on the terminal portion of the adapter; and the female screw-thread extends from a bottom of the concave conical surface formed in the interchangeable cutting member; wherein the first convex conical surface and the second concave conical surface are configured and arranged for mutually centering said adapter and said interchangeable cutting member, when the adapter and the interchangeable cutting member are screwed together; and wherein said first axial abutment surface and said second axial abutment surface are mutually engageable for axially positioning the interchangeable cutting member and the adapter one with respect to the other when said interchangeable cutting member and said adapter are screwed together.