PILOT Problem Set 11.pdf - Math 202 Pilot Problem set 11 week of April 18 1 Find the surface area of the part of the paraboloid z = x2 y 2 with z 1 2 A

PILOT Problem Set 11.pdf - Math 202 Pilot Problem set 11...

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Math 202 Pilot Problem set 11, week of April 18 1. Find the surface area of the part of the paraboloid z = x 2 + y 2 with z 1. 2. A surface of revolution is obtained by rotating a curve x = f ( u ) > 0 , z = g ( u ) , a u b in the xz plane about the z axis. If v denotes the (polar) angle of rotation, then a parametrization for the resulting surface is given by ~ X ( u, v ) = < f ( u ) cos v, f ( u ) sin v, g ( u ) > . Find a formula for the area of the surface. 3. Show that the area you obtained in question 2 is equal to 2 π xL where L is the length of the curve and x is the average x coordinate. 4. A torus T is obtained by taking the curve to be a circle. Take
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  • Fall '07
  • WILSON
  • Calculus, Surface, Prism

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