Engineering Board Exam Reviewer · Applications: Centroid, Work, and Moment of Inertia · medium

The region bounded by y=x2, y=9, and the y-axis is revolved about the y-axis to form a solid paraboloid. How far is its centroid from the vertex, along the axis?

  1. 9/2
  2. 6
  3. 27/4
  4. 3

Answer

B. 6

Solution

The disk area at height y is π x2=π y. y= 09y·π y,dy/ 09π y,dy=243/81/2=6 (that is, 23h).

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