How to Calculate and Solve the Centre of Gravity of a Segment of a Sphere

The image above represents a segment of a sphere.
To compute the centre of gravity of a segment of a sphere requires two essential parameters. These parameters are the radius of the sphere and height of the segment of the sphere.

The formula for computing the centre of gravity of a sphere is:

C.G. = 3(2r – h)² / 4(3r – h)

Where:
C.G. = Centre of Gravity
r = Radius of the Sphere
h = Height of the Segment of the Sphere

Let’s solve an example
Find the centre of gravity of the segment of the sphere where the radius of the sphere is 10 m and the height of the segment of the sphere is 4 m.

This implies that:
r = Radius of the Sphere = 10
h = Height of the Segment of the Sphere = 4

C.G. = 3(2(10) – 4)² / 4(3(10) – 4)
C.G. = 3(20 – 4)² / 4(30 – 4)
C.G. = 3(16)² / 4(26)
C.G. = 3(256) / 104
C.G. = 768 / 104
C.G. = 7.38

Therefore, the centre of gravity of the segment of the sphere is 7.38.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the centre of gravity of a segment of a sphere at a height, h at a distance from the centre of the sphere measured along the height.

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