For constants h,p> 0 let r = 2ph and consider the plane domain D in the...
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For constants h,p> 0 let r = √2ph and consider the plane domain D in the first quadrant, bounded by x² = 2py, x = 0 and y = h. (a) Show that the area of D is A = 2rh/3 and that the x-coordinate of its centroid is x = 3r/8. (b) Consider the solid paraboloid of revolution T of radius r and height h, obtained by revolving the plane domain D around the y-axis. Use the first theorem of Pappus to show that the volume of T is V = r²h/2. For constants h,p> 0 let r = √2ph and consider the plane domain D in the first quadrant, bounded by x² = 2py, x = 0 and y = h. (a) Show that the area of D is A = 2rh/3 and that the x-coordinate of its centroid is x = 3r/8. (b) Consider the solid paraboloid of revolution T of radius r and height h, obtained by revolving the plane domain D around the y-axis. Use the first theorem of Pappus to show that the volume of T is V = r²h/2.
Expert Answer:
Answer rating: 100% (QA)
a To find the area of D we can integrate y from 0 to h and x from 0 to 2py A 0h02py dx dy 0h 2py dy ... View the full answer
Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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