Finding Centroid of 4 Sections: Help Needed

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SUMMARY

The discussion focuses on calculating the centroid of a composite shape consisting of two semicircles, one rectangle, and one right triangle in the xz plane. The user correctly identified the individual centroids (x, y, z) for each section and multiplied them by their respective areas. However, the final centroid calculation appears to be incorrect, indicating a potential error in the summation of the products or the total area used in the division. Detailed verification of the calculations is required to identify the source of the error.

PREREQUISITES
  • Understanding of centroid calculations in composite shapes
  • Knowledge of area formulas for semicircles, rectangles, and triangles
  • Familiarity with coordinate systems, specifically the xz plane
  • Basic algebra for summation and division operations
NEXT STEPS
  • Review the formulas for calculating the centroid of semicircles, rectangles, and triangles
  • Practice calculating centroids of composite shapes with varying dimensions
  • Learn about the integration method for finding centroids in complex shapes
  • Explore software tools like MATLAB or GeoGebra for visualizing centroid calculations
USEFUL FOR

Students and professionals in engineering, architecture, and physics who are involved in geometric calculations and centroid determination for various shapes.

jukos
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Homework Statement
centroid of a body consisting of two planes
Relevant Equations
centroid of semi circle = (4R / 3 pi, 4R / 3 pi)
centroid of rectangle = (b/2, h/2)
centroid of triangle = (b/3, h/3)
I found the centroid of four sections, 2 semicircles, 1 rectangle (xz plane) and the remaining right triangle.
I tabulated the individual centroids (x,y,z) of the 4 sections, multiplied each one with the Area of respective section. In the end I calculated the required (x,y,z) by dividing (sum of xA) by (total area of body). I'm getting wrong answer, Please help
 
Last edited:
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Could you show us your work in detail?
What the right answer should be?
 

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