# HW 13 - Math E-21a Fall 2009 HW#13 problems To be turned in...

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1 Math E-21a – Fall 2009 – HW #13 problems To be turned in Thurs, Dec 10 : Section 12.6 : 2. Find the area of the part of the plane 2 5 10 x y z that lies inside the cylinder 2 2 9 x y . 4. Find the area of the part of the plane with vector equation ( , ) 1 , 2 , 3 5 u v v u v u v r that is given by 0 1, 0 1 u v . 6. Find the area of the part of the surface 2 1 3 2 z x y that lies above the triangle with vertices (0,0), (0,1), and (2,1). 10. Find the area of the part of the paraboloid 2 2 x y z that lies inside the cylinder 2 2 9 y z . [ Hint : Try modifying the method for a graph ( , ) z f x y for this case where we have ( , ) x f y z .] 24. The figure shows the surface created when the cylinder 2 2 1 y z intersects the cylinder 2 2 1 x z . Find the area of this surface. [ Hint : Find the surface area of one of the eight identical pieces of this surface, e.g. the part above the triangular region bounded by the lines y x , y x   , and 1 x .] 28. The figure shows the torus obtained by rotating about the z -axis the circle in the xz -plane with center ( ,0,0) b and radius a b . Parametric equations for the torus are cos cos cos sin cos sin sin x b a y b a z a where and are the angles shown in the figure. Find the surface area of the torus. Section 13.6 : 8. Evaluate the surface integral S xy dS  where S is the triangular region with vertices (1,0,0) , (0,2,0) , and (0,0,2) . [ Note : The surface S is a portion of a plane.] 12. Evaluate the surface integral

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• Fall '09
• -
• Math, Surface, 4 k

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