Find the area of the part of the plane 5x 2y z 10 that li

Find the area of the part of the plane 5x + 2y + z = 10 that lies inside the cylinder x^2 + y^2 = 4.

Rewrite the equation of the plane as z = 10 - 5x - 2y. Let R denote the region bounded in x^2 + y^2 = 4. Using Cartesian Coordinates, the surface area equals ??R v[1 + (z_x)^2 + (z_y)^2] dA = ??R v[1 + (-5)^2 + (-2)^2] dA = ??R v30 dA = v30 * (Area inside x^2 + y^2 = 4) = v30 * (p * 2^2) = 4pv30. = 68.79