A copper [k = 390 J/(s·m·C°)] pipe with an outer radius of 0.014 m runs from an outdoor wall faucet into the interior of a house. The temperature of the faucet is 1.0°C, and the temperature of the pipe, 3.1 m from the faucet, is 30°C. In fifteen minutes, the pipe conducts a total of 230 J of heat to the outdoor faucet from the house interior. Find the inner radius of the pipe. Ignore any water inside the pipe.