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Present a problem with solution solving the centroid of a solid of revolution using the circular ring method.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter7: Locus And Concurrence

Section7.2: Concurrence Of Lines

Problem 20E

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Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?
Present a problem with solution solving the centroid of a solid of revolution using the circular disc method
Show complete solution, please. 2. Present a problem with a solution solving the centroid of a solid of revolution using the circular ring method.
Assuming the result that the centroid of a solid hemisphere lies on the axis of symmetry three-eighths of the way from the base toward the top, show, by trans-forming the appropriate integrals, that the center of mass of a solid semiellipsoid (x2/a2) + (y2/b2) + (z2/c2)<=1, z >= 0, lies on the z-axis three-eighths of the way from the base toward the top. (You can do this without evaluating any of the integrals.)
Show complete solution, please. 1. Present a problem with a solution solving the centroid of a solid of revolution using the circular disc method.
A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that has its vertex at one corner of ℛ and passes through the opposite corner. Find the centroids of both ℛ1 and ℛ2.
Show that the centroid of the solid semiellipsoid of revolution (r2/a2 ) + (z2/h2 )<=1, z>=0, lies on the z-axis three-eighths of the way from the base to the top. The special case h = a gives a solid hemisphere. Thus, the centroid of a solid hemisphere lies on the axis of symmetry three-eighths of the way from the base to the top.