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Re: Centroid of 3 Lines or triangle
Using Vertical Strip
V=Σ[2π∫x2x1xydx]
V=2π∫20x(3x−x)dx+2π∫42x[(8−x)−x]dx
V=32π unit3
By symmetry
XG=0
Solving for YG
VYG=Σ[2π∫x2x1ycxydx]
VYG=Σ[2π∫x2x112(yU+yL)x(yU−yL)dx]
VYG=Σ[π∫x2x1x(yU2−yL2)dx]
32πYG=π∫20x(9x2−x2)dx+π∫42x[(8−x)2−x2]dx
32πYG=3523π
YG=113
Centroid of the solid is at (0, 11/3)
Re: Centroid of volume formed by rotating about the y-axis...
Using Horizontal Strip
V=Σ[π∫x2x1(xR2−xL2)dy]
V=π∫40(y2−19y2)dy+π∫64[(8−y)2−19y2)]dy
V=32π unit3
VYG=Σ[π∫x2x1yc(xR2−xL2)dy]
32πYG=π∫40y(y2−19y2)dy+π∫64y[(8−y)2−19y2)]dy
32πYG=3523π
YG=113
Centroid of the solid is at (0, 11/3)