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Home Applications of the Integral Area of a Surface of Revolution Problems  
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In Problems 112, find the area of the surface generated by rotating the given curve about the yaxis. first quadrant In Problems 1320, find the area of the surface generated by rotating the given curve about the xaxis. 21 The part of the circle x^{2} + y^{2} = r^{2} between x = 0 and x = a in the first quadrant is rotated about the xaxis. Find the area of the resulting zone of the sphere (0 < a < r). 22 Solve the above problem when the rotation is about the yaxis. In Problems 2326 set up integrals for the areas generated by rotating the given curve about (a) the y^{:}axis, (b) the xaxis. 27 Set up an integral for the area generated by rotating the curve y = jx^{2}, 0 < x < 1 about the xaxis and find the Trapezoidal Approximation with Δx = 0.2. 28 Set up an integral for the area generated by rotating the curve y = jx^{3}, 0 < x < 1 about the yaxis and find the Trapezoidal Approximation with Δx = 0.2. 29 Show that the surface area of the torus generated by rotating the circle of radius r and center (c, 0) about the yaxis (r < c) is A = 4π^{2}rc. Hint: Take y as the independent variable and use the formula for the length of the arc of the circle from y = a to y = b.


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