An above-ground circular swimming pool is heated so that it can be used in cool weather. The ground has a temperature of 10°C far from the pool. The heater is turned on and quickly brings the pool water to a comfortable 20°C; assume this is the temperature of the circular region of the ground beneath the swimming pool. The pool has a diameter of 5 m.

(a) Calculate the rate of heat transfer from the pool to the ground, ten hours after the heater is turned on.

(b) Calculate the time it would take for the heat transfer rate to reach within 10% of its steady-state value.