A copper [k = 390 J/(s•m•C°)] pipe with an outer radius of 0.014 meter runs from an outdoor wall faucet into the interior of a house. The temperature of the faucet is 2.0°C, and the temperature of the pipe, 3.1 meter from the faucet, is 29°C. In fifteen minutes, the pipe conducts a total of 270 Joule of heat to the outdoor faucet from the house interior. Evaluate the inner radius of the pipe. Neglect any water inside the pipe.