Answered: Locate the centroid of the shaded area…

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Locate the centroid of the shaded area shown in each of the following figures. if h = 12 in. and h = 8 in

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.72P: Locate the centroid of the volume generated by revolving the area shown about the line AB. Use...

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Question

Locate the centroid of the shaded area shown in each of the
following figures.
if h = 12 in. and h = 8 in

Expert Solution

Step 1

Given,

$b = 12 i n h = 8 i n$

Step 2

The triangle has right-angle at the origin. Therefore the centroid is at a distance of $b / 3$ along x-axis and $h / 3$ along y-axis.

$\bar{x} = \frac{b}{3} = \frac{12 i n}{3} = 4 i n \bar{y} = \frac{h}{3} = \frac{8 i n}{3} = 2.66 i n$

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