Problem 4.21 A lamp shade is designed by drawing a curve and then rotating it about the z axis, forming a "surface of revolution. " It is desired that the lamp shade have the minimum possible surface area. Obtain the functional for this problem. See Figure 4.15 to get an idea of the geometry. axis Curve of length s ds Area of shaded region is 27 x ds

Problem 4.21 A lamp shade is designed by drawing a curve and then rotating it about the z axis, forming a "surface of revolution. " It is desired that the lamp shade have the minimum possible surface area. Obtain the functional for this problem. See Figure 4.15 to get an idea of the geometry. axis Curve of length s ds Area of shaded region is 27 x ds

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