GNG Centroid Equations

Arc Segment

r = rsinalpha/alpha

Quarter and Semicircular Arcs

y = 2r/pi

Circular Area

r = r

Semicircular Area

y = 4r/3pi

Quarter Circular Area

x = y = 4r/3pi

Area of Circular Sector

x = (2/3)(rsinalpha/alpha)

Rectangular Area

x = 1/2(x) and y = 1/2(y)

Triangular Area

x = (a+b)/3 y = h/3

Area of Ellipitical Quadrant

x = 4a/3pi y = 4b/3pi

Subparabolic Area (A= (ab)/3)

x = 3a/4 y = 3b/10

Parabolic Area (A=(2ab)/3)

x = 3a/8 y =3b/5

Half Cylindrical Shell

x = 2r/pi

Semicylinder

x = 4r/3pi

Hemispherical Shell

x = r/2

Quarter Ciruclar Rod

x = y = 2r/pi

Conical Shell

z = 2h/3

Half Conical Shell

x = 4r/3pi y = 2h/3

Right Cirular Cone

z = 3h/4

Half Cone

x = r/h z = 3h/4

Semiellipsoid

z = 3c/8

Ellpitic Paraboloid

z = 2c/3

Rectangular Tetrahedron

x = a/4 y = b/4 z = c/4

Half Torus

x = (a² + 4R²)/(2piR)