A hollow pure aluminum sphere with an electrical heater in the center is used in tests at steady-state conditions to determine the thermal conductivity of insulating materials. The inner diameter of the sphere is 0.350m; the outer diameter is 0.400m. For this test, the inner surface temperature of the pure aluminum sphere is held at a constant temperature of 250.0°C. The pure aluminum sphere is uniformly covered with an insulating material, 0.0900m thick. The outside surface of the insulating material is exposed to convection; Tᵢnf = 22.0°C, hᵢnf = 25.0 W/(m²-K) The power required to keep the inner surface of the sphere at 250.0°C is 85.0W (this is assumed to be equal to the heat transfer rate, q) Ignoring contact resistance, determine the thermal conductivity of the insulating material, k.