As a result of radioactive decay, heat is generated uniformly throughout the interior of the earth at a rate of around 30 watts per cubic kilometer. (a watt is a rate of heat production.) the heat then fows to the earth's surface where it is lost to space. let f(z, y, 2) denote the rate of flow of heat measured in watts per square kilometer. by definition, the fu of facross a surface is the quantity of heat flowing through the surface per unit of time. (a) suppose that the actual heat generation is 30w /kin3 what is the value of div f div f (include units.) (b) assume the heat tlows outward symmetrically. verify that f-or where r-zi + yj + zk and α is a suitable constant. satisfies the given conditions. find a include units) c) let t z y z denote the temperature inside the earth. heat ows according to the equation f sphere with radius 6400 km and surface temperature 20°c, what is the temperature at the center? -k grad t where kis a constant. lf t s in c then k 30 000 с/km assuming the earth is a (degrees c)