$\mathrm{<img\; src="https://dsd5zvtm8ll6.cloudfront.net/questions/2024/04/662a5a460f669\_1714051653570.jpg"\; style="width:\; 64.86\%;\; display:\; block;\; vertical-align:\; top;\; margin:\; 5px\; auto;\; text-align:\; center;"\; width="64.86\%"\; height="274"\; alt="(1)\; Let\; a,\; b\; >0\; with\; b\; >\; a.\; Consider\; a\; planet"> }$

(1) Let a, b >0 with b > a. Consider a planet of radius r = a. Suppose that the planet is covered in a layer of ice of height h = b - a, so that the outer radius of the ice r = b, i.e. the distance from the center of the planet to the outer tip of the ice sitting on the surface of the planet is equal to b. If the density of the ice is given by ho (x, y, z) = z2 px 2 + y 2 +z2, then find the mass of the layer of ice that is covering the planet. Hint: Use spherical coordinates, and note that the layer of ice covering the planet is contained within the region of radius a < = r < = b. (1) Let a, b >0 with b> a. Consider a planet of radius r = a. Suppose that the planet is covered in a layer of ice of height h = b-a, so that the outer radius of the ice r = b, i.e. the distance from the center of the planet to the outer tip of the ice sitting on the surface of the planet is equal to b. If the density of the ice is given by ho (x, y, z) = ( z^(2))/((Ox^(2)+y^(2)+z^ (2))), then find the mass of the layer of ice that is covering the planet. Hint: Use spherical coordinates, and note that the layer of ice covering the planet is contained within the region of radius a < = r < = b.