2. Sketch S & R, and evaluate the surface area.
a. Evaluate the surface (S) area of the paraboloid $z = x^2 + y^2$ below $z = 1$.
b. Find the surface (S) area of the portion of the plane $z = 2 - x - y$
That lies above the circle $x^2 + y^2 \le 1$ in the first quadrant.
3. Find the mass of the surface lamina S of density p. $m = \iint_S \rho(x, y, z)dS$
a. S: $2x + 3y + 6z = 12$, first octant, $\rho(x, y, z) = x^2 + y^2$
b. A cone-shaped surface lamina S is given by $z = 4 - 2\sqrt{x^2 + y^2}$, $0 \le z \le 4$
At each point on S, the density is proportional to the distance between the point and
z-axis, i.e. $\rho(x, y, z) = k\sqrt{x^2 + y^2}$.
Find the mass m of the lamina $m = \iint_S \rho(x,y,z)dS$.