A nuclear reactor core has melted down into a 1m diameter sphere and has sunk through the ground to a centerline depth of 20m. The melted core is internally generating heat at a constant intrinsic rate of 8105W/m3. The ground has a thermal conductivity of 1.6 W/mC and a surface temperature held constant at 25C. Note: spheres have a volume of 4/3r3 and surface area of 4r2 a) What is the total heat generation rate in watts? ( 10 points) b) What would be the steady-state surface temperature of the core? (15 points)