A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y. z) = 35 - 7(x' + y + z") "C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat flow across a surface S within the solid is given by -K /s Vwds. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 k W/(m . K)). (Use symbolic notation and fractions where needed.) -K Vwds = kW S