Çözüldü Centroid of A Solid of Revolution - The Second Theorem of Pappus

https://i.ibb.co/0qxjHWv/Centroid.png
https://scontent.fada2-2.fna.fbcdn....=086593d5b76f3c55476dcdb95c86a73a&oe=5ED72FFE
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"When the area is revolved about x-axis, the centroid C(x1, y1, z1) is on that axis. Which means that, for solids generated by revolving the plane area about an axis, its centroid is on that axis, thus, giving one coordinate."
https://www.slideshare.net/phaxawayako28/lesson-14-centroid-of-volume
(Page 4)

According to the Second Theorem of Pappus, "the volume of a solid of revolution obtained by rotating a lamina F about a non-intersecting axis lying in the same plane is equal to the product of the area A of the lamina F and the distance d traveled by the centroid of F"
https://www.math24.net/pappus-theorem/

Volume = (lower limit x1 = 0, upper limit x2 = 4),∫ π·[ (6x)^2 - x^2 ] dx = 2240π / 3 cubic units
https://www.wolframalpha.com/input/...n y=6x and y=x revolved around x axis 0<=x<=4

Area = (lower limit x1 = 0, upper limit x2 = 4),∫ (6x - x) dx = 40 square units
V = A·d = A·(2π·R) = A·(2π·x1)
2240π / 3 = 40·2π·x1
x1 = 28 / 3 units
y1 = z1 = 0