MATH 2163 Quiz: MATH 2163 OK State Quiz4
Document Summary
Quiz # 10 math 2163, calculus iii nov. 9, 2007. Show all your work neatly and concisely, and indicate your nal answer clearly: find the area of the part of the plane. 2x + 5y + z = 10 that lies inside the cylinder x2 + y2 = 9. Solution: the formula for the surface area is. Zzdqf 2 x + f 2 y + 1 da where d is given by the cylinder that the surface lies in. In this problem, the easiest way to describe d, the disk inside x2 + y2 = 9, is to use polar coordinates: D = {(r, ) | 0 2 , 0 r 3}. The surface is given by 2x + 5y + z = 10, which means z = f (x, y) = 10 2x 5y, fy = 5. fx = 2, Zzdqf 2 x + f 2 y + 1 da = zzdp( 2)2 + ( 5)2 + 1 da.
