6. Evaluate using spherical coordinate
$$ \int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{\sqrt{8-x^2-y^2}} (x^2 + y^2 + z^2) \,dzdydx. $$
[7 marks]
7. Find the mass of the solid in the shape of tetrahedron that is bounded by the planes $$ x + y + z = 1 $$, xy-plane, xz-plane and yz-plane if its density is given by $$ \delta(x, y, z) = x $$.
[6 marks]