Surface Area Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the surface area of the surface of the portion of the plane that lies in he first octant.

(2) Find the surface area of the surface of the portion of the paraboloid that lies inside the cylinder

(3) Find the surface area of the surface of the portion of the plane that is above the square in the plane with vertices and   

(4) Find the surface area of the surface of the portion of the surface that lies over the triangular region in the plane with vertices and   

(5) Find the surface area of the surface of the portion of the sphere inside the cylinder

(6) Find the surface area of the surface of the portion of the cone inside the cylinder

(7) Find the surface area of the surface of the portion of the sphere inside the cylinder and above the -plane.

(8) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the triangle with vertices

(9) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the square and

(10) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the disk

(11) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the disk

(12) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the region in the -plane bounded by the curve and the line

(13) Setup, but do not evaluate, the double integral for the surface area of the portion of the surface given by over the region in the -plane bounded by

(14) Compute the magnitude of the fundamental cross product for the surface defined parametrically by

(15) Compute the magnitude of the fundamental cross product for the surface defined parametrically by

(16) Compute the magnitude of the fundamental cross product for the surface defined parametrically by

(17) Compute the magnitude of the fundamental cross product for the surface defined parametrically by

(18) Find the area of the surface given parametrically by the equation



for

(19) A spiral ramp has the vector parametric equation



for Find the surface area of this ramp.

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