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

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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 25 1 0 xy z  that lies inside the cylinder 22 9  . 4. Find the area of the part of the plane with vector equation (,) 1 , 2,3 5 uv vu v u v  r that is given by 01 ,   . 6. Find the area of the part of the surface 2 13 2 zx 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 x yz that lies inside the cylinder 9 . [ Hint : Try modifying the method for a graph (, ) zf x y for this case where we have (,) x fyz .] 24. The figure shows the surface created when the cylinder 1 intersects the cylinder 1 xz . 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 ab . Parametric equations for the torus are cos cos cos sin cos sin sin xb a yb a za       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 xydS  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 S zdS where S is the surface 2 2,0 1 ,0 1 x y z
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This note was uploaded on 02/10/2011 for the course MATH E-21a taught by Professor - during the Fall '09 term at Harvard.

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

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